{"id":33674,"date":"2021-10-23T08:02:13","date_gmt":"2021-10-23T02:32:13","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=33674"},"modified":"2021-10-23T08:02:33","modified_gmt":"2021-10-23T02:32:33","slug":"04-04-00q","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/04-04-00q\/","title":{"rendered":"\u0db4\u0dd4\u0d82\u0da0\u0dd2 \u0d85\u0db7\u0dd2\u0dba\u0ddd\u0d9c\u0dba\u0d9a\u0dca!"},"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:#fba96e;min-height:471px;aspect-ratio:unset;\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#7b3605;font-size:20px\"><strong>\u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba (0,0) \u0dc0\u0db1 <span class=\"wp-katex-eq\" data-display=\"false\">y=e^{-x^2}\\;\u0dc4\u0dcf\\;y=-e^{-x^2}<\/span> \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0db1\u0dca \u0d85\u0dad\u0dbb \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0db1 \u0dc0\u0dd2\u0dc1\u0dcf\u0dbd\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/10\/04.04_img-01.jpg\" alt=\"\" class=\"wp-image-33673\" width=\"558\" height=\"209\" \/><\/figure><\/div>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<p style=\"font-size:20px\">\u00a0\u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0db1\u0dca \u0d85\u0dad\u0dbb \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0db1 \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba (0,0) \u0dc0\u0db1 \u0dc0\u0dd2\u0dc1\u0dcf\u0dbd\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd3\u0db8 \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0dc3\u0dd2\u0dad\u0dcf \u0db6\u0dbd\u0db8\u0dd4.<br>\u0d91\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0db1\u0dca \u0d89\u0d9a\u0dca\u0db8\u0dc0\u0dcf \u0db1\u0ddc\u0dba\u0dcf \u0dc0\u0d9a\u0dca\u200d\u0dbb \u0dc3\u0dca\u0db4\u0dbb\u0dca\u0dc1 \u0d9a\u0dbb\u0db8\u0dd2\u0db1\u0dca \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"382\" height=\"147\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/10\/image-16.png\" alt=\"\" class=\"wp-image-33676\" \/><\/figure><\/div>\n\n\n\n<p style=\"font-size:20px\">\u0db8\u0dd4\u0dbd\u0dd2\u0db1\u0dca\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba \u0d9c\u0dab\u0db1\u0dba \u0d9a\u0dbb\u0db8\u0dd4.<\/p>\n\n\n\n<p style=\"font-size:20px\">\u0dc3\u0db8\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0dc3\u0dd0\u0dbd\u0d9a\u0dd3\u0db8\u0dd9\u0db1\u0dca <span class=\"wp-katex-eq\" data-display=\"false\">y=e^{-x^2}<\/span> (\u0db0\u0db1 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba) \u0d87\u0dc3\u0dd4\u0dbb\u0dd4 \u0d9a\u0dbb\u0d9c\u0dd9\u0db1 \u0d85\u0dbb\u0dba \u0dc3\u0ddc\u0dba\u0db8\u0dd4.<\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">(x,e^{-x^2})<\/span> ,<span class=\"wp-katex-eq\" data-display=\"false\">y=e^{-x^2}<\/span>\u00a0\u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba \u0db8\u0dad \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd2 \u0d95\u0db1\u0dd1\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/p>\n\n\n\n<p style=\"font-size:20px\">\u0db8\u0dd6\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0dc0\u0db1 <span class=\"wp-katex-eq\" data-display=\"false\">O\\equiv(0,0)<\/span> \u0dc3\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">(x,e^{-x^2})<\/span> \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dd2 \u0d85\u0dc0\u0db8 \u0daf\u0dd4\u0dbb \u0d85\u0db4\u0da7 \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0d9a\u0dbb\u0db1 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba\u0da7 \u0dc3\u0db8\u0dcf\u0db1 \u0dc0\u0dd9\u0db1\u0dc0\u0dcf.<\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}(0,0)\\;\u0dc3\u0dd2\u0da7\\;(x,e^{-x^2})\\;\u0daf\u0d9a\u0dca\u0dc0\u0dcf\\;\u0daf\u0dd4\u0dbb\\;&amp;=&amp;\\sqrt{(x-0)^2+(e^{-x^2}-0)^2}\\\\&amp;=&amp;\\sqrt{x^2+e^{-2x^2}}\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\">\u0d91\u0dc0\u0dd2\u0da7 , <span class=\"wp-katex-eq\" data-display=\"false\">(0,0)<\/span> \u0dc3\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">(x,e^{-x^2})<\/span> \u0db1\u0db8\u0dca, <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}r&amp;=&amp;\\sqrt{x^2+e^{-2x^2}}\\end{array}<\/span> \u0dc4\u0dd2 \u0d85\u0dc0\u0db8\u0dba <\/p>\n\n\n\n<p style=\"font-size:20px\">\u0db8\u0dd9\u0dc4\u0dd2 \u0d85\u0dc0\u0db8 r \u0d85\u0d9c\u0dba \u0dbd\u0db6\u0dcf \u0d9c\u0dd0\u0db1\u0dd3\u0db8\u0da7 \u0d89\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba \u0d9a\u0dc5 \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2. \u0dc0\u0dbb\u0dca\u0d9c\u0db8\u0dd6\u0dbd\u0dba \u0dc3\u0db8\u0d9f \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba \u0da7\u0dd2\u0d9a\u0d9a\u0dca \u0d85\u0db4\u0dc4\u0dc3\u0dd4\u0dba\u0dd2. \u0db8\u0dda \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0\u0dda\u0daf\u0dd3 \u0dc0\u0dd9\u0db1\u0dad\u0dca \u0db4\u0dc4\u0dc3\u0dd4 \u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba\u0d9a\u0dca \u0dba\u0ddc\u0daf\u0dcf \u0d9c\u0db1\u0dca\u0db1 \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca.<br>\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba\u0da7 \u0db0\u0db1 \u0d85\u0d9c\u0dba\u0d9a\u0dca \u0db4\u0db8\u0dab\u0d9a\u0dca \u0db4\u0dc0\u0dad\u0dd2\u0db1 \u0db1\u0dd2\u0dc3\u0dcf \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba\u0da7 \u0db4\u0dd9\u0dbb \u0d89\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0dda \u0daf\u0dd9\u0db4\u0dc3\u0db8 \u0dc0\u0dbb\u0dca\u0dbd \u0d9a\u0dbb\u0db1\u0dca\u0db1 \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca.<\/p>\n\n\n\n<p style=\"font-size:20px\">\u0d91\u0dc0\u0dd2\u0da7 , <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}r^2&amp;=&amp;x^2+e^{-2x^2}\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\">\u0daf\u0dd9\u0db4\u0dc3\u0db8 x \u0dc0\u0dd2\u0dc1\u0dba\u0dd9\u0db1\u0dca \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba\u0dd9\u0db1\u0dca,<\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac{d(r^2)}{dx}&amp;=&amp;2x+e^{-2x^2}.(-2)2x\\\\&amp;=&amp;2x-4xe^{-2x^2}\\\\&amp;=&amp;2x(1-2e^{-2x^2})\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac{d(r^2)}{dx}&amp;=&amp;0\\end{array}<\/span>\u0dc0\u0dd2\u0da7 x \u0dc4\u0dd2 \u0d85\u0dc0\u0db8 \u0d85\u0d9c\u0dba \u0dbd\u0dd0\u0db6\u0dda. <\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}2x(1-2e^{-2x^2})&amp;=&amp;0\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}(1-2e^{-2x^2})&amp;=&amp;0\\\\1&amp;=&amp;2e^{-2x^2}\\\\1&amp;=&amp;\\frac2{e^{2x^2}}\\\\e^{2x^2}&amp;=&amp;2\\\\e^{x^2}&amp;=&amp;\\sqrt2\\\\x^2&amp;=&amp;\\ln\\sqrt2\\end{array}<\/span> \u0dc4\u0ddd <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}2x&amp;=&amp;0\\\\x&amp;=&amp;0\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}x&amp;=&amp;0\u0dc0\u0dd2\u0da7,r^2=0+e^0=1\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">x^2=ln2<\/span> \u0dc0\u0dd2\u0da7, <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}r^2&amp;=&amp;\\ln\\sqrt2+\\frac12\\\\&amp;\\approx&amp;0.847&lt;1\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}x^2&amp;=&amp;\\ln\\sqrt2\\;\u0dc0\u0dd2\u0da7\\;r^2\\end{array}<\/span> \u0d85\u0dc0\u0db8 \u0d85\u0d9c\u0dba\u0d9a\u0dca \u0d9c\u0db1\u0dca\u0db1\u0dc0\u0dcf.<\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;r^2\\end{array}<\/span> \u0d85\u0dc0\u0db8 \u0dc0\u0dd2\u0da7 r \u0daf \u0d85\u0dc0\u0db8 \u0dc0\u0dd9\u0db1\u0dc0\u0dcf.<\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda\\;\u0d85\u0dbb\u0dba&amp;=&amp;\\sqrt{\\ln\\sqrt2+\\frac12}\\end{array}<\/span><\/p>\n\n\n\n<p style=\"font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda\\;\u0dc0\u0dbb\u0dca\u0d9c\u0db5\u0dbd\u0dba&amp;=&amp;\\pi r^2\\\\&amp;=&amp;\\pi(\\ln\\sqrt2+\\frac12)\\end{array}<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0\u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0db1\u0dca \u0d85\u0dad\u0dbb \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0db1 \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba (0,0) \u0dc0\u0db1 \u0dc0\u0dd2\u0dc1\u0dcf\u0dbd\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd3\u0db8 \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3 \u0dc3\u0dd2\u0dad\u0dcf \u0db6\u0dbd\u0db8\u0dd4.\u0d91\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba\u0db1\u0dca \u0d89\u0d9a\u0dca\u0db8\u0dc0\u0dcf \u0db1\u0ddc\u0dba\u0dcf \u0dc0\u0d9a\u0dca\u200d\u0dbb \u0dc3\u0dca\u0db4\u0dbb\u0dca\u0dc1 \u0d9a\u0dbb\u0db8\u0dd2\u0db1\u0dca \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2. \u0db8\u0dd4\u0dbd\u0dd2\u0db1\u0dca\u0db8 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba \u0d9c\u0dab\u0db1\u0dba \u0d9a\u0dbb\u0db8\u0dd4. \u0dc3\u0db8\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0dc3\u0dd0\u0dbd\u0d9a\u0dd3\u0db8\u0dd9\u0db1\u0dca (\u0db0\u0db1 \u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba) \u0d87\u0dc3\u0dd4\u0dbb\u0dd4 \u0d9a\u0dbb\u0d9c\u0dd9\u0db1 \u0d85\u0dbb\u0dba \u0dc3\u0ddc\u0dba\u0db8\u0dd4. ,\u00a0\u0dc0\u0d9a\u0dca\u200d\u0dbb\u0dba \u0db8\u0dad \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd2 \u0d95\u0db1\u0dd1\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0d9a\u0dca \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4. \u0db8\u0dd6\u0dbd \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0dc0\u0db1 \u0dc3\u0dd2\u0da7 \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dd2 \u0d85\u0dc0\u0db8 \u0daf\u0dd4\u0dbb \u0d85\u0db4\u0da7 [&hellip;]<\/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-33674","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\/33674"}],"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=33674"}],"version-history":[{"count":5,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/33674\/revisions"}],"predecessor-version":[{"id":33695,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/33674\/revisions\/33695"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=33674"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=33674"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=33674"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}