{"id":34791,"date":"2022-02-21T07:13:02","date_gmt":"2022-02-21T01:43:02","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=34791"},"modified":"2022-02-21T07:13:05","modified_gmt":"2022-02-21T01:43:05","slug":"04-05-06q","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/04-05-06q\/","title":{"rendered":"\u0d94\u0db6\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf?"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\"><\/div>\n\n\n\n<div class=\"wp-block-cover has-background-dim\" style=\"background-color:#b1cbdf\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#38556d;font-size:20px\">&nbsp;<strong><span class=\"wp-katex-eq\" data-display=\"false\">x\\geq1<\/span> \u0dc3\u0db3\u0dc4\u0dcf <span class=\"wp-katex-eq\" data-display=\"false\">y=\\frac1x<\/span> \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba x \u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dc3\u0dd1\u0daf\u0dd9\u0db1 \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0 \u0dc3\u0dbd\u0d9a\u0db1\u0dca\u0db1.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"535\" height=\"233\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/11\/04.05.06_img_Gaberiels_horn.jpg\" alt=\"\" class=\"wp-image-34789\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-color\" style=\"color:#38556d;font-size:20px\"><strong>1.\u0d91\u0db8 \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.( <span class=\"wp-katex-eq\" data-display=\"false\">y=f(x)<\/span> \u0dc0\u0db1 \u0d9d\u0dd8\u0dab \u0db1\u0ddc\u0dc0\u0db1 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dca x \u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dc3\u0dd1\u0daf\u0dd9\u0db1 \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0 \u0db8\u0dd9\u0db8 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dbd\u0db6\u0dcf \u0daf\u0dda. <span class=\"wp-katex-eq\" data-display=\"false\">v=\\mathrm\\pi\\int_{\\mathrm a}^{\\mathrm b}{\\mathrm f{(\\mathrm x)}^2}\\;\\mathrm{dx}\\;;\\;\\mathrm a\\leq\\mathrm x\\leq\\mathrm b<\/span> )<\/strong><\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#38556d;font-size:20px\"><strong>2.<span class=\"wp-katex-eq\" data-display=\"false\">y=f(x)<\/span> \u0dc0\u0db1 \u0d9d\u0dd8\u0dab \u0db1\u0ddc\u0dc0\u0db1 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dca x \u0d85\u0d9a\u0dca\u0dc2\u0dba \u0dc0\u0da7\u0dcf \u0db7\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0dc3\u0dd1\u0daf\u0dd9\u0db1 \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0d9a \u0db8\u0dad\u0dd4\u0db4\u0dd2\u0da7 \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0db4\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0dd9\u0db1\u0dca \u0dbd\u0db6\u0dcf \u0daf\u0dda.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left has-text-color\" style=\"color:#38556d;font-size:20px\"><strong><span class=\"wp-katex-eq\" data-display=\"false\">A=2\\mathrm\\pi\\int_{\\mathrm a}^{\\mathrm b}\\mathrm f(\\mathrm x)\\;\\sqrt{1+{{\\mathrm f^\/(\\mathrm x)}}^2}\\;\\mathrm{dx}\\;;\\;\\mathrm a\\leq\\mathrm x\\leq\\mathrm b<\/span><\/strong><br><strong>\u0d89\u0dc4\u0dad \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1\u0dca \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0\u0da7 \u0d85\u0dc3\u0dd3\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u0d9a\u0dca \u0dc4\u0dcf \u0dc3\u0dd3\u0db8\u0dd2\u0dad \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\u0d9a\u0dca \u0d87\u0dad\u0dd2 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p style=\"font-size:20px\">&nbsp;<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}1.\u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\\;&amp;=&amp;\\mathrm\\pi\\int_1^\\infty\\left(\\frac1{\\mathrm x}\\right)^2\\;\\mathrm{dx}\\\\&amp;=&amp;\\mathrm\\pi\\int_1^\\infty\\frac1{\\mathrm x^2}\\;\\mathrm{dx}\\\\&amp;=&amp;\\mathrm\\pi\\int_1^\\infty\\mathrm x^{-2}\\;\\mathrm{dx}\\\\&amp;=&amp;\\mathrm\\pi\\left[-\\mathrm x^{-1}\\right]_1^\\infty\\\\&amp;=&amp;-\\mathrm\\pi\\left[\\frac1{\\mathrm x}\\right]_1^\\infty\\\\&amp;=&amp;-\\mathrm\\pi\\left(\\frac1\\infty-\\frac11\\right)\\\\&amp;=&amp;\\mathrm\\pi\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}2.f(x)&amp;=&amp;\\frac1x\\\\&amp;&amp;x\\;\u0dc0\u0dd2\u0dc2\u0dba\u0dd9\u0db1\u0dca\\;\u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba\u0dd9\u0db1\u0dca,\\\\f^{&#039;}(x)\\;&amp;=&amp;-1x^{-2}\\\\&amp;=&amp;-\\frac1{x^2}\\\\\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba&amp;=&amp;2\\pi\\;\\int_1^\\infty\\frac1x\\sqrt{1+\\left(-\\frac1{x^2}\\right)^2}\\;dx\\\\\\sqrt{1+\\left(-\\frac1{x^2}\\right)^2}&amp;&lt;&amp;1\\;\u0db1\u0dd2\u0dc3\u0dcf,\\\\\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba&amp;=&amp;2\\mathrm\\pi\\int_1^\\infty\\frac1{\\mathrm x}\\mathrm{dx}\\\\\\mathrm A&amp;=&amp;2\\mathrm\\pi\\left[\\mathrm{lnx}\\right]_1^\\infty\\\\&amp;=&amp;2\\mathrm\\pi\\left[\\ln\\infty-\\ln1\\right]\\\\\\mathrm A&amp;\\rightarrow&amp;\\infty\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\">\u0d92 \u0d85\u0db1\u0dd4\u0dc0 \u0db8\u0dd9\u0db8 \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0 \u0d9d\u0dab \u0d92\u0d9a\u0d9a <span class=\"wp-katex-eq\" data-display=\"false\">\\mathrm\\pi<\/span> \u0dc0\u0db1 \u0dc3\u0dd3\u0db8\u0dd2\u0dad \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\u0d9a\u0dd2\u0db1\u0dca \u0dc4\u0dcf <span class=\"wp-katex-eq\" data-display=\"false\">\\infty<\/span> \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0daf\u0dd2\u0dc0\u0dd9\u0db1 \u0d85\u0dc3\u0dd3\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dc3\u0db8\u0db1\u0dca\u0dc0\u0dd2\u0dad \u0dc0\u0dda.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; \u0d92 \u0d85\u0db1\u0dd4\u0dc0 \u0db8\u0dd9\u0db8 \u0d9d\u0dab \u0dc0\u0dc3\u0dca\u0dad\u0dd4\u0dc0 \u0d9d\u0dab \u0d92\u0d9a\u0d9a \u0dc0\u0db1 \u0dc3\u0dd3\u0db8\u0dd2\u0dad \u0db4\u0dbb\u0dd2\u0db8\u0dcf\u0dc0\u0d9a\u0dd2\u0db1\u0dca \u0dc4\u0dcf \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0daf\u0dd2\u0dc0\u0dd9\u0db1 \u0d85\u0dc3\u0dd3\u0db8\u0dd2\u0dad \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dc3\u0db8\u0db1\u0dca\u0dc0\u0dd2\u0dad \u0dc0\u0dda.<\/p>\n","protected":false},"author":73,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[6067,42,3629],"tags":[],"class_list":{"0":"post-34791","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-infinite-thinking","7":"category-advanced-level-science","8":"category-combined-mathematics"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/34791"}],"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\/73"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=34791"}],"version-history":[{"count":16,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/34791\/revisions"}],"predecessor-version":[{"id":35671,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/34791\/revisions\/35671"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=34791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=34791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=34791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}