{"id":16242,"date":"2021-05-27T10:35:51","date_gmt":"2021-05-27T05:05:51","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=16242"},"modified":"2022-01-25T12:06:10","modified_gmt":"2022-01-25T06:36:10","slug":"04-01-00","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/04-01-00\/","title":{"rendered":"04.01.00 &#8211; \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc3\u0dd3\u0db8\u0dcf\u0dc0"},"content":{"rendered":"\r\n<p><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?export=download&amp;id=1DcsVYUeaDGzb-qxx2l-nNw4V9J0s353n\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/p>\r\n<p>&nbsp;<\/p>\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"has-inline-color has-vivid-red-color\">\u0dc3\u0d82\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba I \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda A \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dbd\u0d9a\u0dd4\u0dab\u0dd4 25 \u0d9a \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a\u0dca \u0db8\u0dd9\u0db8 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0d9a\u0dbb \u0d87\u0dad.<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<div class=\"wp-block-media-text is-stacked-on-mobile has-background\" style=\"background-color: #d8b2eb;grid-template-columns: 16% auto\">\r\n<figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"878\" class=\"wp-image-32670 size-full\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/10\/04.01_Into_Archimedes-1.jpg\" alt=\"\" \/><\/figure>\r\n<div class=\"wp-block-media-text__content\">\r\n<p>\u0db4\u0dd4\u0dbb\u0dcf\u0dab \u0d9c\u0dca\u200d\u0dbb\u0dd3\u0d9a \u0d9c\u0dab\u0dd2\u0dad\u0da5\u0dba\u0d9a\u0dd4 \u0dc0\u0dd6 Archimedes \u0dc0\u0dd2\u0dc3\u0dd2\u0db1\u0dca \u0dc0\u0d9a\u0dca\u200d\u0dbb \u0dc4\u0dd0\u0da9\u0dba\u0db1\u0dca \u0db8\u0dd0\u0db1\u0dd3\u0db8 \u0dc4\u0dcf \u0d9c\u0ddd\u0dbd\u0dba\u0d9a \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0db8\u0dd0\u0db1\u0dd3\u0db8 \u0dba\u0db1 \u0d9a\u0dbb\u0dd4\u0dab\u0dd4 \u0db8\u0dd4\u0dbd\u0dca \u0d9a\u0dbb \u0d9c\u0dd9\u0db1 \u0d9a\u0dca\u200d\u0dbb\u0dd2.\u0db4\u0dd6. 3 \u0dc0\u0db1 \u0dc3\u0dd2\u0dba\u0dc0\u0dc3\u0dda \u0daf\u0dd3 \u0dc3\u0dd3\u0db8\u0dcf \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0db4\u0dad\u0dca \u0d9a\u0dc5 \u0db8\u0dd4\u0dbd\u0dca\u0db8 \u0d85\u0daf\u0dc4\u0dc3 1906 \u0daf\u0dd3 \u0d9c\u0dab\u0dd2\u0dad\u0da5\u0dba\u0dd2\u0db1\u0dca \u0dc0\u0dd2\u0dc3\u0dd2\u0db1\u0dca \u0dc3\u0ddc\u0dba\u0dcf \u0d9c\u0db1\u0dca\u0db1\u0dcf \u0dad\u0dd9\u0d9a\u0dca \u0dc3\u0dd0\u0d9f\u0dc0\u0dd3 \u0db4\u0dd0\u0dc0\u0dad\u0dd2\u0dab\u0dd2. \u0db8\u0dd9\u0dbd\u0dd9\u0dc3 Archimedes \u0d9c\u0dda \u0dc3\u0d82\u0d9a\u0dbd\u0dca\u0db4 20 \u0dc0\u0db1 \u0dc3\u0dd2\u0dba\u0dc0\u0dc3 \u0dad\u0dd9\u0d9a\u0dca \u0dc3\u0dd0\u0d9f\u0dc0 \u0db4\u0dd0\u0dc0\u0dad\u0dd2 \u0db1\u0dd2\u0dc3\u0dcf, \u0dc3\u0dd3\u0db8\u0dcf \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dc0 \u0db1\u0dd6\u0dad\u0db1 \u0d9c\u0dab\u0dd2\u0dad \u0dc3\u0d82\u0d9a\u0dbd\u0dca\u0db4 \u0dc0\u0dbb\u0dca\u0db0\u0db1\u0dba \u0dc0\u0dd6\u0dba\u0dda \u0dc0\u0dd9\u0db1\u0dad\u0dca \u0d9c\u0dab\u0dd2\u0dad\u0da5\u0dba\u0db1\u0dca\u0d9c\u0dda \u0d85\u0daf\u0dc4\u0dc3\u0dca \u0d85\u0db1\u0dd4\u0dc3\u0dcf\u0dbb\u0dba\u0dd9\u0db1\u0dd2.<\/p>\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dca\u0dc0\u0dcf\u0dba\u0d9a\u0dca\u0dad \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0d9a\u0dd2\u0dc3\u0dd2\u0dba\u0db8\u0dca \u0d85\u0d9c\u0dba\u0d9a\u0dca \u0d9a\u0dbb\u0dcf \u0d86\u0dc3\u0db1\u0dca\u0db1 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0d91\u0db1\u0dd4 \u0dbd\u0db6\u0db1 \u0d85\u0d9c\u0dba \u0d91\u0db8 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0\u0dda \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0dda \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}f\\left(x\\right)<\/span> \u0dba\u0db1\u0dca\u0db1\u0dd9\u0dc4\u0dd2 \u0d85\u0daf\u0dc4\u0dc3 ,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0 x\u00a0 \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba a\u00a0 \u0d9a\u0dbb\u0dcf \u0d86\u0dc3\u0db1\u0dca\u0db1 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 f (x)\u00a0 \u0dc4\u0dd2 \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u0dba\u0db1\u0dca\u0db1\u0dba\u0dd2.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab : &#8211;<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u00a001)\u00a0\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow1}<\/span><strong>( x<sup>2 <\/sup>+ 2x + 1 ) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 02)\u00a0\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\frac{\\mathrm\\pi}3}<\/span><strong>( sinx + cosx )<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0 = (1) <sup>2<\/sup> + 2(1) +1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = sin<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac\\pi3<\/span><strong>+cos<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac\\pi3<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0 = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\sqrt3}2+\\frac12<\/span><strong>\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\sqrt3+1}2<\/span><strong>\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a003)\u00a0\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow2}\\frac{x^2-4}{x+5}<\/span><strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 04)\u00a0\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\infty}\\frac1{5x+2}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{4-4}{2+5}<\/span><strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 = <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1{5\\infty+2}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1\\infty<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 =\u00a0 0<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab 01 \u0dc3\u0dbd\u0d9a\u0db8\u0dd4. x \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba 1 \u0d9a\u0dbb\u0dcf \u0d86\u0dc3\u0db1\u0dca\u0db1 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7\u00a0 <strong>( x<\/strong><strong><sup>2 <\/sup><\/strong><strong>+ 2x + 1 ) <\/strong>\u0dc4\u0dd2 \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u0dba\u0db1\u0dca\u0db1 \u0db8\u0dd9\u0dc4\u0dd2 \u0d85\u0daf\u0dc4\u0dc3\u0dba\u0dd2. \u0d91\u0dc0\u0dd2\u0da7 \u0db8\u0dd9\u0db8 \u0d9c\u0dd0\u0da7\u0dbd\u0dd4\u0dc0 \u0dc0\u0dd2\u0dc3\u0daf\u0dd3\u0db8\u0dda\u0daf\u0dd3 x \u0d87\u0dad\u0dd2 \u0dad\u0dd0\u0db1\u0dca \u0dc0\u0dbd\u0da7 1 \u0dba\u0ddc\u0daf\u0dcf \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0 \u0dc0\u0dd2\u0dc3\u0daf\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d9c\u0dab\u0dd2\u0dad\u0dba\u0dda\u0daf\u0dd3 \u0db1\u0dd2\u0dbb\u0dca\u0dab\u0dba \u0d9a\u0dc5 \u0db1\u0ddc\u0dc4\u0dd0\u0d9a\u0dd2 \u0d9c\u0dab\u0dd2\u0dad \u0d9a\u0dbb\u0dca\u0db8 \u0d85\u0db1\u0dd2\u0dbb\u0dca\u0dab\u0dd3\u0dba \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf \u0db1\u0db8\u0dca \u0dc0\u0dda,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dd3\u0db8\u0dcf \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dbd\u0daf\u0dd3\u0daf \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc3\u0dd3\u0db8\u0dcf \u0db1\u0ddc\u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf \u0dc4\u0dd9\u0dc0\u0dad\u0dca \u0d85\u0db1\u0dd2\u0dbb\u0dca\u0dab\u0dd3\u0dba \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf \u0db4\u0dc0\u0dad\u0dd3.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc3\u0dd3\u0db8\u0dcf \u0db1\u0ddc\u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf ,<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab : &#8211;<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a001)\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow1}\\frac{x^2-1}{x-1}<\/span><strong> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 02) \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow2}\\frac{x^3-8}{x^2-5x+6}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{1-1}{1-1}<\/span><strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{8-8}{4-5+6}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{0}{0}<\/span><strong> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{0}{5}<\/span><strong>\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong>\u0d85\u0db1\u0dd2\u0dbb\u0dca\u0dab\u0dd3\u0dba \u0dc0\u0dda<strong> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = <\/strong>\u0d85\u0db1\u0dd2\u0dbb\u0dca\u0dab\u0dd3\u0dba \u0dc0\u0dda<strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a003)\u00a0 <\/strong>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow2}\\frac{2x^2-5x+2}{x^2-3x+2}<\/span><strong> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/strong>\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{2\\left(2\\right)^2-5\\left(2\\right)+2}{x^2-3\\left(2\\right)+2}<\/span> <strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{8-10+2}{4-6+2}<\/span><strong>\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=<\/strong> <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{0}{0}<\/span><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong>\u0d85\u0db1\u0dd2\u0dbb\u0dca\u0dab\u0dd3\u0dba \u0dc0\u0dda<strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d8b\u0daf\u0dc4\u0dbb\u0dab <strong>\u00a001) <\/strong>\u0dc3\u0dbd\u0d9a\u0db8\u0dd4. x\u00a0 \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba <strong>1<\/strong>\u00a0 \u0d9a\u0dbb\u0dcf \u0dba\u0db1 \u0dc0\u0dd2\u0da7 \u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{x^2-1}{x-1}<\/span> \u00a0 \u0dc4\u0dd2 \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u0dba\u0db1\u0dca\u0db1 \u0db8\u0dd9\u0dc4\u0dd2 \u0d85\u0daf\u0dc4\u0dc3\u0dba\u0dd2. x \u0da7 <strong>1<\/strong>\u00a0 \u0dba\u0dd9\u0daf\u0dd4 \u0dc0\u0dd2\u0da7 \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb <span class=\"wp-katex-eq\" data-display=\"false\">\\frac00 <\/span>\u0dc0\u0dda. \u0db8\u0dd9\u0db8 \u0db1\u0dd2\u0dc3\u0dcf \u0db8\u0dd9\u0db8 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0 \u0dc3\u0dd3\u0db8\u0dcf\u0dc0\u0d9a\u0dca \u0db1\u0ddc\u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a\u0dca \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u0d9c\u0dd0\u0db1 \u0dc3\u0d9a\u0da0\u0dca\u0da1\u0dcf \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dda\u0daf\u0dd3 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0db1\u0dca \u0d9a\u0dd2\u0dc4\u0dd2\u0db4\u0dba\u0d9a\u0dca \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0daf\u0dc0 \u0d85\u0db0\u0dca\u200d\u0dba\u0dba\u0db1\u0dba \u0d9a\u0dd9\u0dbb\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>K\u00a0 \u0db1\u0dd2\u0dba\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7,<\/li>\r\n<\/ol>\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0 f(x) = k<\/strong> \u0dba\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u0d91\u0dc0\u0dd2\u0da7 <strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span><\/strong> <strong>f(x) = k<\/strong> <strong>\u00a0<\/strong>\u0dc0\u0dda.\u00a0<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"2\">\r\n<li>K\u00a0 \u0db1\u0dd2\u0dba\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7 ,<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 <strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span><\/strong><strong>k f(x)\u00a0 = k<\/strong> <strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span><\/strong> <strong>f(x)<\/strong><\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"3\">\r\n<li>\u00a0<strong> <span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span>[ f (x ) <span class=\"wp-katex-eq\" data-display=\"false\">\\pm<\/span> g ( x) ] =\u00a0<\/strong> \u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span> f(x)\u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\pm<\/span><\/strong> \u00a0<\/strong> \u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span> g(x)<\/strong><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"4\">\r\n<li>\u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span> [<sup>\u00a0 <\/sup>f(x).g ( x)\u00a0 ]\u00a0 \u00a0 =<\/strong> <strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span> f(x).<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span><\/strong>g(x)<\/strong><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"5\">\r\n<li>\u00a0<strong> g(x) \u2260 0<\/strong> \u0db1\u0db8\u0dca, \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{f(x)}{g(x)}<\/span> \u00a0 <strong>\u00a0 =\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\lim_{x\\rightarrow\\alpha}f(x)}{\\lim_{x\\rightarrow\\alpha}g(x)}<\/span><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"6\">\r\n<li><strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span>[ f(x) ] <\/strong><sup>\u00a0n <\/sup>\u00a0= <strong>[ <span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span><\/strong> <strong>\u00a0 f(x) ] <\/strong><sup>\u00a0n <\/sup>\u00a0\u00a0<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"7\">\r\n<li><strong>f(x) 0 <\/strong>\u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\sqrt[n]{f(x)}=\\sqrt[n]{\\lim_{x\\rightarrow\\alpha}f(x)}<\/span><strong> \u00a0 \u00a0 <\/strong><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"8\">\r\n<li>\u0dc3\u0dd2\u0dba\u0dbd\u0dd4 x \u20ac R \u0dc3\u0daf\u0dc4\u0dcf f \u0db6\u0dc4\u0dd4 \u0db4\u0daf \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7 ,<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span>f(x)\u00a0 \u00a0 = f(a)<\/strong><\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"9\">\r\n<li>a\u00a0 \u0d87\u0dad\u0dd4\u0dc5\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dba\u0d9a x = a\u00a0 \u0dc4\u0dd2\u0daf\u0dd3 \u0dc4\u0dd0\u0dbb \u0dc3\u0dd2\u0dba\u0dbd\u0dd4 x \u0dc3\u0daf\u0dc4\u0dcf<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>f(x) = g(x) <\/strong>\u0db1\u0db8\u0dca <strong>, <\/strong>\u0d91\u0dc0\u0dd2\u0da7<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span>f(x)\u00a0 \u00a0 = \u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}<\/span><\/strong>g(x)\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><strong>n \u0db7\u0dcf\u0d9c \u0dc3\u0d82\u0d9b\u0dca\u200d\u0dba\u0dcf\u0dc0\u0d9a\u0dca \u0dc0\u0dd2\u0da7,<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>n = <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{p}{q}<\/span> \u00a0 \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<p>p \u0dc4\u0dcf q\u00a0 \u0db1\u0dd2\u0d9b\u0dd2\u0dbd \u0dc0\u0dda,<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\left(\\frac{x^n-\\alpha^n}{x-\\alpha}\\right)=\\lim_{x\\rightarrow\\alpha}\\frac{x^{\\displaystyle\\frac pq}-\\alpha^{\\displaystyle\\frac pq}}{x-\\alpha}<\/span> <strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{x^{\\left(\\frac1q\\right)p}-\\alpha^{\\left(\\frac1q\\right)p}}{x-\\alpha}<\/span> <strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{x^{\\left(\\frac1q\\right)p}-\\alpha^{\\left(\\frac1q\\right)p}}{x^{\\left(\\frac1q\\right)q}-\\alpha^{\\left(\\frac1q\\right)q}}<\/span><strong>\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong><span class=\"wp-katex-eq\" data-display=\"false\">x^\\frac1q<\/span> = X\u00a0 \u00a0 \u0daf,\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\alpha^\\frac1q<\/span> = A\u00a0 \u0daf \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db8\u0dd4.<\/strong><\/p>\r\n\r\n\r\n\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">x\\rightarrow\\alpha<\/span>\u00a0 \u0dc0\u0dd2\u0da7\u00a0 \u00a0<span class=\"wp-katex-eq\" data-display=\"false\">X\\rightarrow A<\/span>\u00a0 \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{x^n-\\alpha^n}{x-\\alpha}=\\lim_{X\\rightarrow A}\\frac{X^p-A^p}{X^q-A^q}<\/span> <strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{X\\rightarrow A}\\frac{X^p-A^p}{X-A}\\times\\frac{X-A}{X^q-A^q}<\/span> <strong>\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{X\\rightarrow A}\\frac{X^p-A^p}{X-A}\\;\\lim_{X\\rightarrow A}\\frac1{\\frac{X^q-A^q}{X-A}}<\/span> <strong>\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{pA^{p-1}}{qA^{q-1}}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac pqA^{p-q}<\/span><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac pqa^{\\frac1q\\left(p-q\\right)}<\/span><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac pqa^{\\frac pq-1}<\/span><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>= na<\/strong><strong><sup> n \u2013 1<\/sup><\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-cover has-background-dim\" style=\"background-color: #7983f3\">\r\n<div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\r\n<p class=\"has-text-align-center has-text-color\" style=\"color: #163846;font-size: 20px\"><strong>\u0d94\u0db6 \u0d9c\u0db8\u0db1\u0d9a\u0dca \u0dba\u0dcf\u0db8\u0da7 \u0d86\u0dbb\u0db8\u0dca\u0db7\u00a0 \u0d9a\u0dbd\u0dcf \u0dba\u0dd0\u0dba\u0dd2 \u0dc3\u0dd2\u0dad\u0db1\u0dca\u0db1. \u0d94\u0db6 \u0d9c\u0db8\u0db1\u0dda \u0db8\u0dd4\u0dc5\u0dd4 \u0daf\u0dd4\u0dbb\u0dd9\u0db1\u0dca\u00a0 \u0d9a\u0dca \u0d9c\u0dd9\u0dc0\u0dcf \u0d9c\u0dd2\u0dba \u0db4\u0dc3\u0dd4 \u0d94\u0db6\u0da7 \u0dad\u0dc0\u00a0 \u0d9a \u0daf\u0dd4\u0dbb\u0d9a\u0dca \u0d9c\u0db8\u0db1\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0da7 \u0d89\u0dad\u0dd4\u0dbb\u0dd4\u0dc0 \u0dad\u0dd2\u0db6\u0dd9\u0db1\u0dc0\u0dcf. \u0d91\u0dad\u0dd0\u0db1\u0dca \u0dc3\u0dd2\u0da7 \u0dad\u0dc0\u00a0 \u0d9a\u0dca \u0d9c\u0db8\u0db1\u0dca \u0d9a\u0dbd \u0dc0\u0dd2\u0da7 \u0d94\u0db6\u0da7 \u0dad\u0dc0\u0daf\u0dd4\u0dbb\u0da7\u0dad\u0dca, \u0db8\u0dd4\u0dc5\u0dd4 \u0daf\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0d9a\u0dca \u0d9c\u0db8\u0db1\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0da7 \u0d89\u0dad\u0dd4\u0dbb\u0dd4\u0dc0 \u0dad\u0dd2\u0db6\u0dd9\u0db1\u0dc0\u0dcf. \u0db8\u0dd9\u0dbd\u0dd9\u0dc3 \u0dc3\u0dd1\u0db8 \u0dc0\u0dd2\u0da7\u0db8 \u0d94\u0db6\u0da7 \u0db8\u0dd4\u0dc5\u0dd4 \u0daf\u0dd4\u0dbb\u0dd9\u0db1\u0dca <span class=\"wp-katex-eq\" data-display=\"false\">\\frac12\u0d9a\u0dca,\\;\\;\\frac14\\;\u0d9a\u0dca,\\;\\;\\frac18\\;\u0d9a\u0dca,\\frac1{16}\\;\u0d9a\u0dca\\dots.\\;<\/span> \u0dba\u0db1\u0dcf\u0daf\u0dd3\u00a0 \u0dc0\u0dc1\u0dba\u0dd9\u0db1\u0dca \u0dad\u0dc0\u0dad\u0dca \u0d9a\u0ddc\u0da7\u0dc3\u0d9a\u0dca \u0d9c\u0db8\u0db1\u0dca \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0da7 \u0d89\u0dad\u0dd4\u0dbb\u0dd4 \u0dc0\u0dd9\u0dbd\u0dcf \u0dad\u0dd2\u0dba\u0dd9\u0db1\u0dc0\u0dcf.<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-32750\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/10\/04.01-Question-1.png\" alt=\"\" width=\"463\" height=\"220\" \/><\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n<p class=\"has-text-color\" style=\"color: #163846;font-size: 20px\"><strong>\u0db8\u0dd9\u0dc4\u0dd9\u0db8 \u0db6\u0dd0\u0dbd\u0dd4\u0dc0\u0ddc\u0dad\u0dca \u0d9a\u0ddc\u0da0\u0dca\u0da0\u0dbb \u0daf\u0dd4\u0dbb \u0d9c\u0dd2\u0dba\u0dad\u0dca \u0dad\u0dc0\u0dad\u0dca \u0d9a\u0ddc\u0da7\u0dc3\u0d9a\u0dca \u0d9c\u0db8\u0db1\u0dca \u0d9a\u0dbb\u0db1\u0dca\u0db1 \u0d89\u0dad\u0dd4\u0dbb\u0dd4 \u0dc0\u0dd9\u0dbd\u0dcf \u0dad\u0dd2\u0dba\u0db1\u0dc0\u0dcf \u0db1\u0dda\u0daf?<br \/>\u0d9a\u0dc0\u0daf\u0dcf\u0dc0\u0dad\u0dca \u0db8\u0dda \u0d9c\u0db8\u0db1 \u0d85\u0dc0\u0dc3\u0db1\u0dca \u0d9a\u0dbb\u0db1\u0dca\u0db1 \u0db6\u0dd0\u0dbb\u0dd2 \u0dc0\u0dd9\u0db1\u0dc0\u0dcf \u0db1\u0dda\u0daf?<br \/>\u0dc3\u0dd3\u0db8\u0dcf \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0daf\u0dd0\u0db1\u0dd4\u0db8 \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0db8\u0dda \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1\u0dba\u0da7 \u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1 \u0d94\u0dba\u0dcf\u0da7 \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf?<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link has-background\" style=\"border-radius: 10px;background: linear-gradient(135deg,#0693e3 0%,#163846 0%)\" href=\"https:\/\/learnsteer.sasnaka.org\/science\/?p=32751\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><strong>( 13.3 ) \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0daf\u0dd3\u0db8 \u0dc3\u0daf\u0dc4\u0dcf \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\left(\\frac{x^n-\\alpha^n}{x-\\alpha}\\right)<\/span> \u00a0<strong> = na<sup>n &#8211; 1 <\/sup>\u00a0\u00a0\u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dcf \u0d9a\u0dd2\u0dbb\u0dd3\u0db8.<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba : &#8211;\u00a0 <strong>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\left(\\frac{x^n-\\alpha^n}{x-\\alpha}\\right)<\/span><\/strong> \u00a0<strong> = na<sup>n &#8211; 1 <\/sup>\u00a0\u00a0<\/strong>\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0 \u0dc3\u0dcf\u0db0\u0db1\u0dba :-\u00a0<\/p>\r\n<p>\u00a0\u00a0\u00a0 n \u0db0\u0db1 \u0db1\u0dd2\u0d9b\u0dd2\u0dbd\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7 ,<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0f(x) = x<\/strong><strong><sup>n <\/sup><\/strong><strong>\u00a0&#8211; a<\/strong><strong><sup>n<\/sup><\/strong> \u00a0\u0dba\u0dd2 \u0d9c\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = a<\/strong> \u0dc0\u0dd2\u0da7\u00a0 <strong>f(x)\u00a0 = a<\/strong><strong><sup>n <\/sup><\/strong><strong>\u00a0&#8211; a<\/strong><strong><sup>n <\/sup><\/strong><strong>\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 0<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u0d91\u0db1\u0db8\u0dca\u00a0 ( x \u2013 a ) \u0dc3\u0dcf\u0db0\u0d9a\u0dba\u0d9a\u0dd2.<\/p>\r\n\r\n\r\n\r\n<p>\u0d91\u0d9a\u0db8 \u0dbb\u0da7\u0dcf\u0dc0\u0d9a\u0da7 \u0d9c\u0dad\u0dca \u0dc0\u0dd2\u0da7,<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{x^n-\\alpha^n}{x-\\alpha}<\/span>\u00a0 = x<sup> n &#8211; 1<\/sup>\u00a0 + ax <sup>n &#8211; 2<\/sup>\u00a0 + a<sup>2<\/sup>x <sup>n &#8211; 3<\/sup> + \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.. + a <sup>n &#8211; 1<\/sup> x\u00a0 + \u00a0 a <sup>n &#8211; 1<\/sup>\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{x^n-\\alpha^n}{x-\\alpha}<\/span><\/strong>\u00a0<strong> =\u00a0<\/strong> \u00a0<strong> x<sup> n &#8211; 1<\/sup>\u00a0 + ax <sup>n &#8211; 2<\/sup>\u00a0 + a<sup>2<\/sup>x <sup>n &#8211; 3<\/sup> + \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.. + \u00a0 a <sup>n &#8211; 1<\/sup>\u00a0 ]\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= a <\/strong><strong><sup>n &#8211; 1<\/sup><\/strong><strong> \u00a0 + a <\/strong><strong><sup>n &#8211; 1<\/sup><\/strong><strong> \u00a0 + a <\/strong><strong><sup>n &#8211; 1<\/sup><\/strong><strong> \u00a0 + \u2026\u2026\u2026\u2026\u2026\u2026\u2026. + a <\/strong><strong><sup>n &#8211; 1<\/sup><\/strong><strong>\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><strong>n a <\/strong><strong><sup>n &#8211; 1<\/sup><\/strong><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><strong>n \u0d9d\u0dd8\u0dab \u0db1\u0dd2\u0d9b\u0dd2\u0dbd\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7,<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0n = &#8211; m \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0n \u20ac z<sup>&#8211; \u00a0 <\/sup>\u0db1\u0dd2\u0dc3\u0dcf\u00a0 m \u20ac z<sup>+<\/sup><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\left(\\frac{x^n-\\alpha^n}{x-\\alpha}\\right)<\/span><\/strong><\/strong>\u00a0<strong>\u00a0 =\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{x^{-m}-\\alpha^{-m}}{x-\\alpha}<\/span> \u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{x^\\frac1m-\\alpha^\\frac1m}{x-\\alpha}<\/span> \u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{\\alpha^m-x^m}{x^m\\alpha^m\\left(x-\\alpha\\right)}<\/span> \u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{-1}{x^m\\alpha^m}\\times\\frac{{\\displaystyle x}^m-\\alpha^m}{\\left(x-\\alpha\\right)}<\/span><strong>\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>=\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow\\alpha}\\frac{-1}{x^m\\alpha^m}\\times\\lim_{x\\rightarrow\\alpha}\\frac{{\\displaystyle x}^m-\\alpha^m}{\\left(x-\\alpha\\right)}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{-1}{\\alpha^m\\alpha^m}\\times m\\alpha^{m-1}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">-m\\alpha^{-m-1}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 \u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">n\\alpha^{n-1}<\/span><\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab : &#8211;<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow2}\\frac{x^3-8}{x-2}=\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^3-2^3}{\\displaystyle x-2}<\/span> \u00a0<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 3(2)<\/strong><strong><sup>2<\/sup><\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong><sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/sup>= \u00a0 3 x 4<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><strong>=\u00a0 12<\/strong><\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"2\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow1}\\frac{x^\\frac53-1}{x-1}=\\lim_{x\\rightarrow1}\\frac{\\displaystyle x^\\frac{\\displaystyle5}{\\displaystyle3}-1^\\frac{\\displaystyle5}{\\displaystyle3}}{\\displaystyle x-1}<\/span>\u00a0<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac53\\left(1\\right)^{\\frac53-1}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac53\\times1<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac53<\/span><\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"3\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow2}\\frac{x^7-128}{x^5-32}=\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^7-2^7}{\\displaystyle x^5-2^5}<\/span> \u00a0<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^7-2^7}{x-2}}{\\displaystyle\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^5-2^5}{x-2}}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{7(2)^6}{5(2)^4}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{7\\times2^2}5<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle28}5<\/span><\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"4\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow3}\\frac{x^3-27}{x^5-243}=\\lim_{x\\rightarrow3}\\frac{\\displaystyle x^3+3^3}{\\displaystyle x^5+3^5}<\/span> \u00a0<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong>\u00a0<strong>\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^3-\\left(-3^3\\right)}{x^5-\\left(-3^5\\right)}<\/span> \u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>=\u00a0 \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^3-\\left(-3^3\\right)}{x-\\left(-3\\right)}}{\\displaystyle\\lim_{x\\rightarrow2}\\frac{\\displaystyle x^5-\\left(-3^5\\right)}{x-\\left(-3\\right)}}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle3\\left(3\\right)^2}{5\\left(3\\right)^4}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle3}{5\\times9}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle1}{15}<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><strong>( 13.4 ) \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0daf\u0dd3\u0db8 \u0dc3\u0daf\u0dc4\u0dcf \u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle\\sin x}x<\/span><\/strong> ) \u00a0<strong> = 1\u00a0 \u0dc3\u0dd3\u0db8\u0dcf\u0dc0 \u00a0\u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dcf \u0d9a\u0dd2\u0dbb\u0dd3\u0db8.<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p style=\"text-align: left\">\u00a0\u00a0 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba : &#8211; \u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle\\sin x}x<\/span> ) \u00a0<strong> = 1\u00a0 ( <span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span>\u00a0 \u0dbb\u0dda\u0da9\u0dd2\u0dba\u0db1\u0dca )<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u0dc3\u0dcf\u0db0\u0db1\u0dba : <span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span> <strong>&gt; 0 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0 ,<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u0d85\u0dbb\u0dba 1 \u0dc0\u0db1 \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba o \u0dc0\u0db1 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a\u0dca \u0d9c\u0db8\u0dd4.AOB \u2206\u0dc0\u0db1 \u0dbd\u0dd9\u0dc3 \u0db4\u0dbb\u0dd2\u0db0\u0dd2\u0dba \u0db8\u0dad A,B \u0dbd\u0d9a\u0dd4\u0dab\u0dd4 \u0d9a\u0dbb\u0db8\u0dd4. \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2.A \u0dc4\u0dd2\u0daf\u0dd3 \u0d87\u0daf\u0dd3 \u0dc3\u0dca\u0db4\u0dbb\u0dca\u0dc1\u0d9a\u0dba\u0da7 \u0daf\u0dd2\u0d9a\u0dca \u0d9a\u0dbd OB , C \u0dc4\u0dd2\u0daf\u0dd3 \u0dc4\u0db8\u0dd4 \u0dc0\u0dda \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0OAB\u00a0 <\/strong>\u2206<strong>\u00a0 \u00a0 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u00a0 &lt; \u00a0 OAB\u00a0 \u0dc0\u0dd8\u0dad\u0dca\u0dad \u0d9b\u0dab\u0dca\u0da9\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u00a0 &lt; \u00a0 OAC <\/strong>\u2206<strong>\u00a0 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac12<\/span><strong>(1)(1) sin<span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span> \u00a0 &lt;\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac12<\/span><strong> (1)<sup>2<\/sup> \u00a0 &lt;\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac12<\/span><strong> (1)(1) tan<span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span><\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0sin<span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span>\u00a0 &lt;\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span> \u00a0 &lt;\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\sin\\theta}{\\cos\\theta}<\/span>\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00f8 \u00a0 \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dca \u0db1\u0dd2\u0dc3\u0dcf (sin<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span><\/strong> \u00a0 &gt; 0 )\u00a0 sin<strong><span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span><\/strong> \u00a0 \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0db6\u0dd9\u0daf\u0db8\u0dd4.\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">1&lt;\\frac\\theta{\\sin\\theta}&lt;\\frac1{\\cos\\theta}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\theta\\rightarrow0}1&gt;\\lim_{\\theta\\rightarrow0}\\frac{\\sin\\theta}\\theta&gt;\\lim_{\\theta\\rightarrow0}\\cos\\theta<\/span><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">1&gt;\\lim_{\\theta\\rightarrow0}\\frac{\\sin\\theta}\\theta&gt;1<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u0dc3\u0dd0\u0db1\u0dca\u0da9\u0dca\u0dc0\u0dd2\u0da0\u0dca \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad\u0dba \u0d85\u0db1\u0dd4\u0dc0 ,<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\theta\\rightarrow0}\\frac{\\sin\\theta}\\theta=1<\/span><strong>\u00a0\u00a0<\/strong><\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u03b8<strong> &lt; 0 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0 ( \u0d85\u0db4\u0ddd\u0dc4\u0db1\u0dba\u0d9a\u0dd2 )<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u03b8 = <\/strong>-\u03b1<strong> \u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u03b8 &lt; 0 \u0db1\u0dd2\u0dc3\u0dcf <\/strong>-\u03b1<strong> &lt; 0\u00a0 \u00a0 \u00a0\u03b1 <\/strong>&gt;0<strong>\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\theta\\rightarrow0^-}\\frac{\\sin\\theta}\\theta<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{-\\alpha\\rightarrow0^-}\\frac{\\sin\\left(-\\alpha\\right)}{-\\alpha}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{-\\alpha\\rightarrow0^-}\\frac{-\\sin\\alpha}{-\\alpha}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= <\/strong>\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{-\\alpha\\rightarrow0^-}\\frac{\\sin\\alpha}\\alpha<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u00a0 1 ( \u0db8\u0dd4\u0dbd\u0dca \u0d9a\u0ddc\u0da7\u0dc3\u0da7 \u0d85\u0db1\u0dd4\u0dc0 )<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab : &#8211;<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\tan x}x=\\frac{\\sin{\\displaystyle x}}x\\times\\frac1{\\cos{\\displaystyle x}}<\/span><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">1\\times\\frac11<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>=\u00a01<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"2\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\theta\\rightarrow0}\\frac{\\tan\\theta-\\theta}{\\sin\\theta}=\\lim_{\\theta\\rightarrow0}\\frac{\\displaystyle\\sin\\theta-\\theta\\cos\\theta}{\\displaystyle\\sin\\theta\\cos\\theta}<\/span>\u00a0 \u00a0 \u00a0<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\theta\\rightarrow0}\\frac1{\\cos\\theta}-\\lim_{\\theta\\rightarrow0}\\frac\\theta{\\sin{\\displaystyle\\theta}}<\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{\\theta\\rightarrow0}\\frac1{\\cos\\theta}-\\lim_{\\theta\\rightarrow0}\\frac1{\\frac{\\sin\\theta}{\\textstyle\\theta}}<\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>=\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">1-\\frac11<\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>=\u00a0 0<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"3\">\r\n<li>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow0}\\frac{\\sin5x+\\tan7x}{6x}=\\frac16\\lim_{x\\rightarrow0}\\left[\\left(\\frac{\\sin{\\displaystyle5}{\\displaystyle x}{\\displaystyle\\times}{\\displaystyle5}}{5x}\\right)+\\frac{\\sin{\\displaystyle7}{\\displaystyle x}}x\\times\\frac1{\\cos{\\displaystyle7}{\\displaystyle x}}\\right]<\/span> \u00a0\u00a0\u00a0\u00a0\u00a0<strong>\u00a0<\/strong><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>=\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\frac16\\lim_{x\\rightarrow0}\\left[\\left(\\frac{\\sin{\\displaystyle5}{\\displaystyle x}{\\displaystyle\\times}{\\displaystyle5}}{5x}\\right)+\\frac{\\sin{\\displaystyle7}{\\displaystyle x}}{7x}\\times\\frac7{\\cos{\\displaystyle7}{\\displaystyle x}}\\right]<\/span> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\frac16\\left(5+7\\right)<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>=\u00a0 2<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\" start=\"4\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">\\lim_{x\\rightarrow0}\\frac{x+\\sin3x}{x-\\sin3x}=\\lim_{x\\rightarrow0}\\frac{\\displaystyle\\frac{\\displaystyle x}{3x}+\\frac{\\displaystyle\\sin3x}{3x}}{\\displaystyle\\frac{\\displaystyle x}{3x}-\\frac{\\displaystyle\\sin3x}{3x}}<\/span><\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>=\u00a0 <\/strong><span class=\"wp-katex-eq\" data-display=\"false\">\\frac{\\displaystyle\\frac13+1}{\\displaystyle\\frac13-1}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>= &#8211; 2<\/p>\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n<p>\r\n\r\n<\/p>\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?export=download&amp;id=1DcsVYUeaDGzb-qxx2l-nNw4V9J0s353n\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<div>\u00a0<\/div>\r\n<\/div>\r\n<p>\r\n\r\n<\/p>\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\r\n<div class=\"wp-block-buttons is-content-justification-center\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/drive\/folders\/1F2WICHfXx7fonA3FXkduDTBj8pPvPI4-?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n<!-- \/wp:buttons -->\r\n\r\n<!-- wp:spacer -->\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n<\/div>\r\n<p><!-- \/wp:spacer -->\r\n\r\n<!-- wp:buttons --><\/p>\r\n<div class=\"wp-block-buttons\"><!-- wp:button -->\r\n<div class=\"wp-block-button\">\u00a0<\/div>\r\n<\/div>\r\n<!-- \/wp:paragraph -->\r\n\r\n<!-- wp:paragraph {\"align\":\"center\",\"style\":{\"color\":{\"background\":\"#272062\"}}} -->\r\n<p class=\"has-text-align-center has-background\" style=\"background-color: #272062;text-align: center\"><span style=\"color: #ffffff\"><em><strong><span style=\"font-family: 'book antiqua', palatino, serif;font-size: 18pt\">\u201cBe silent unless you can say something that is more useful than your silence.\u201d<\/span><\/strong><\/em><\/span><br \/><span style=\"font-family: tahoma, arial, helvetica, sans-serif;font-size: 10pt;color: #808080\">-Archimedes &#8211;<\/span><\/p>\r\n<!-- \/wp:paragraph -->","protected":false},"excerpt":{"rendered":"<p>\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1. &nbsp; \u0dc3\u0d82\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba I \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda A \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dbd\u0d9a\u0dd4\u0dab\u0dd4 25 \u0d9a \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a\u0dca \u0db8\u0dd9\u0db8 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0dc0\u0dbd\u0dd2\u0db1\u0dca \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0d9a\u0dbb \u0d87\u0dad. \u0db4\u0dd4\u0dbb\u0dcf\u0dab \u0d9c\u0dca\u200d\u0dbb\u0dd3\u0d9a \u0d9c\u0dab\u0dd2\u0dad\u0da5\u0dba\u0d9a\u0dd4 \u0dc0\u0dd6 Archimedes \u0dc0\u0dd2\u0dc3\u0dd2\u0db1\u0dca \u0dc0\u0d9a\u0dca\u200d\u0dbb \u0dc4\u0dd0\u0da9\u0dba\u0db1\u0dca \u0db8\u0dd0\u0db1\u0dd3\u0db8 \u0dc4\u0dcf \u0d9c\u0ddd\u0dbd\u0dba\u0d9a \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0db8\u0dd0\u0db1\u0dd3\u0db8 \u0dba\u0db1 \u0d9a\u0dbb\u0dd4\u0dab\u0dd4 \u0db8\u0dd4\u0dbd\u0dca \u0d9a\u0dbb \u0d9c\u0dd9\u0db1 \u0d9a\u0dca\u200d\u0dbb\u0dd2.\u0db4\u0dd6. 3 \u0dc0\u0db1 \u0dc3\u0dd2\u0dba\u0dc0\u0dc3\u0dda \u0daf\u0dd3 \u0dc3\u0dd3\u0db8\u0dcf \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0db4\u0dad\u0dca \u0d9a\u0dc5 \u0db8\u0dd4\u0dbd\u0dca\u0db8 \u0d85\u0daf\u0dc4\u0dc3 1906 \u0daf\u0dd3 \u0d9c\u0dab\u0dd2\u0dad\u0da5\u0dba\u0dd2\u0db1\u0dca \u0dc0\u0dd2\u0dc3\u0dd2\u0db1\u0dca [&hellip;]<\/p>\n","protected":false},"author":76,"featured_media":16557,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3667,3635,42,3630,3629],"tags":[4581,348,4582,4583,4584],"class_list":{"0":"post-16242","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-04-01-limits","8":"category-04-calculus","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-limits","13":"tag-seemawa","14":"tag-shrithayaka-seemawa","15":"tag-4583","16":"tag-4584"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/16242"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/76"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=16242"}],"version-history":[{"count":50,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/16242\/revisions"}],"predecessor-version":[{"id":35349,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/16242\/revisions\/35349"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media\/16557"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=16242"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=16242"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=16242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}