{"id":4367,"date":"2013-12-16T06:00:36","date_gmt":"2013-12-15T21:00:36","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4367"},"modified":"2014-09-10T16:50:40","modified_gmt":"2014-09-10T07:50:40","slug":"post-4367","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4367","title":{"rendered":"\u30c6\u30fc\u30e9\u30fc\u7d1a\u6570"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000x = a \u306b\u304a\u3051\u308b f(x) \u306e\u30c6\u30fc\u30e9\u30fc\u7d1a\u6570\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%29+%3D+f%28a%29+%2B+f%27%28a%29%28x+-+a%29+%2B+%5Cfrac%7Bf%27%27%28a%29%28x+-+a%29%5E2%7D%7B2%21%7D+%2B+%5Ccdots+%2B+%5Cfrac%7Bf%5E%7Bn+-1%7D%28a%29%28x+-+a%29%5E%7Bn-1%7D%7D%7B%28n+-1%29%21%7D+%2B+R_n&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x) = f(a) + f&#039;(a)(x - a) + \\frac{f&#039;&#039;(a)(x - a)^2}{2!} + \\cdots + \\frac{f^{n -1}(a)(x - a)^{n-1}}{(n -1)!} + R_n' title='\\displaystyle f(x) = f(a) + f&#039;(a)(x - a) + \\frac{f&#039;&#039;(a)(x - a)^2}{2!} + \\cdots + \\frac{f^{n -1}(a)(x - a)^{n-1}}{(n -1)!} + R_n' class='latex' \/>(a)<br \/>\n\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+R_n+%3D+%5Cfrac%7Bf%5En%28x+-+n%29%5En%7D%7Bn%21%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle R_n = \\frac{f^n(x - n)^n}{n!}' title='\\displaystyle R_n = \\frac{f^n(x - n)^n}{n!}' class='latex' \/>, x<sub>0<\/sub> \u306f a \u3068 x \u306e\u7bc4\u56f2\u5185(b)<br \/>\n\u306f reminder \u3068\u547c\u3070\u308c\uff0c f(x) \u304c\u6700\u4f4e\u3067\u3082 n \u6b21\u306e\u5fae\u5206\u4fc2\u6570\u3092\u6301\u3064\u3068\u60f3\u5b9a\u3057\u307e\u3059\uff0en = 1 \u306e\u5834\u5408\u306f\u7279\u306b\u5e73\u5747\u306e\u6cd5\u5247\u307e\u305f\u306f\u5e73\u5747\u5024\u306e\u5b9a\u7406\u3068\u547c\u3070\u308c\uff0c\u6b21\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e<br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7Bf%28x%29+-f%28a%29%7D%7Bx+-+a%7D+%3D+f%27%28x_0%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\frac{f(x) -f(a)}{x - a} = f&#039;(x_0)' title='\\displaystyle \\frac{f(x) -f(a)}{x - a} = f&#039;(x_0)' class='latex' \/>, x<sub>0<\/sub> \u306f a \u3068 x \u306e\u7bc4\u56f2\u5185(c)<\/p>\n<p>\u3000(a) \u306b\u5bfe\u5fdc\u3057\u305f\u7121\u9650\u7d1a\u6570\u306f f(x) \u306e\u6b63\u898f\u30c6\u30fc\u30e9\u30fc\u7d1a\u6570\u3068\u3082\u547c\u3070\u308c\uff0c\u5fc5\u305a\u3042\u308b\u533a\u9593\u306b\u53ce\u675f\u3057\u307e\u3059\uff0e\u4eee\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clim%5Climits_%7Bn+%5Crightarrow+%5Cinfty%7DR_n+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\lim\\limits_{n \\rightarrow \\infty}R_n = 0' title='\\lim\\limits_{n \\rightarrow \\infty}R_n = 0' class='latex' \/> \u304c\u3053\u306e\u533a\u9593\u306b\u3042\u308b\u306a\u3089\uff0e\u3044\u304f\u3064\u304b\u306e\u91cd\u8981\u306a\u30c6\u30fc\u30e9\u30fc\u7d1a\u6570\u3068\u53ce\u675f\u5024\u3092\u305d\u306e\u533a\u9593\u3068\u3068\u3082\u306b\u793a\u3057\u307e\u3059\uff0e<\/p>\n<ol>\n<li><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+e%5En+%3D+1+%2B+x+%2B+%5Cfrac%7Bx%5E2%7D%7B2%21%7D+%2B+%5Cfrac%7Bx%5E3%7D%7B3%21%7D+%2B%5Cfrac%7Bx%5E4%7D%7B4%21%7D+%2B+%5Ccdots%5C+-%5Cinfty+%3C+x+%3C+%5Cinfty%26%2391%3B%2Flatex%26%2393%3B%3C%2Fli%3E++%3Cli%3E%5Blatex%5D%5Cdisplaystyle+%5Csin+x+%3D+x+-+%5Cfrac%7Bx%5E3%7D%7B3%21%7D+%2B+%5Cfrac%7Bx%5E5%7D%7B5%21%7D+-+%5Cfrac%7Bx%5E7%7D%7B7%21%7D+%2B+%5Ccdots%5C+-%5Cinfty+%3C+x+%3C+%5Cinfty%26%2391%3B%2Flatex%26%2393%3B%3C%2Fli%3E++%3Cli%3E%5Blatex%5D%5Cdisplaystyle+%5Ccos+x+%3D+1+-+%5Cfrac%7Bx%5E2%7D%7B2%21%7D+%2B+%5Cfrac%7Bx%5E4%7D%7B4%21%7D+-+%5Cfrac%7Bx%5E6%7D%7B6%21%7D+%2B+%5Ccdots%5C+-%5Cinfty+%3C+x+%3C+%5Cinfty%26%2391%3B%2Flatex%26%2393%3B%3C%2Fli%3E++%3Cli%3E%5Blatex%5D%5Cdisplaystyle+%5Cln%281+%2B+x%29+%3D+x+-+%5Cfrac%7Bx%5E2%7D%7B2%21%7D+%2B+%5Cfrac%7Bx%5E3%7D%7B3%21%7D+-+%5Cfrac%7Bx%5E4%7D%7B4%21%7D+%2B+%5Ccdots%5C+-1+%3C+x+%5Cle+1%26%2391%3B%2Flatex%26%2393%3B%3C%2Fli%3E++%3Cli%3E%5Blatex%5D%5Cdisplaystyle+%5Ctan%5E%7B-1%7Dx+%3D+x+-+%5Cfrac%7Bx%5E3%7D%7B3%21%7D+%2B+%5Cfrac%7Bx%5E5%7D%7B5%21%7D+-+%5Cfrac%7Bx%5E7%7D%7B7%21%7D+%2B+%5Ccdots%5C+-1+%5Cle+x+%5Cle+1&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle e^n = 1 + x + \\frac{x^2}{2!} + \\frac{x^3}{3!} +\\frac{x^4}{4!} + \\cdots\\ -\\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\sin x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots\\ -\\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\cos x = 1 - \\frac{x^2}{2!} + \\frac{x^4}{4!} - \\frac{x^6}{6!} + \\cdots\\ -\\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\ln(1 + x) = x - \\frac{x^2}{2!} + \\frac{x^3}{3!} - \\frac{x^4}{4!} + \\cdots\\ -1 &lt; x \\le 1&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\tan^{-1}x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots\\ -1 \\le x \\le 1' title='\\displaystyle e^n = 1 + x + \\frac{x^2}{2!} + \\frac{x^3}{3!} +\\frac{x^4}{4!} + \\cdots\\ -\\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\sin x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots\\ -\\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\cos x = 1 - \\frac{x^2}{2!} + \\frac{x^4}{4!} - \\frac{x^6}{6!} + \\cdots\\ -\\infty &lt; x &lt; \\infty&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\ln(1 + x) = x - \\frac{x^2}{2!} + \\frac{x^3}{3!} - \\frac{x^4}{4!} + \\cdots\\ -1 &lt; x \\le 1&#091;\/latex&#093;&lt;\/li&gt;  &lt;li&gt;&lt;img src=&#039;https:\/\/s0.wp.com\/latex.php?latex&#038;bg=T&#038;fg=000000&#038;s=0&#039; alt=&#039;&#039; title=&#039;&#039; class=&#039;latex&#039; \/&gt;\\displaystyle \\tan^{-1}x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots\\ -1 \\le x \\le 1' class='latex' \/><\/li>\n<\/ol>\n<p>\u3000\u3042\u308b\u5f62\u306e\u7d1a\u6570 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7Dc_n%28x+-+a%29%5En&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\sum_{n=0}^{\\infty}c_n(x - a)^n' title='\\sum_{n=0}^{\\infty}c_n(x - a)^n' class='latex' \/> \u306f\u3057\u3070\u3057\u3070\u3079\u304d\u7d1a\u6570\u3068\u547c\u3070\u308c\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u3079\u304d\u7d1a\u6570\u306f\u3069\u306e\u533a\u9593\u306b\u3082\u4e00\u69d8\u53ce\u675f\u3057\uff0c\u305d\u308c\u306f\u53ce\u675f\u533a\u9593\u5185\u5168\u4f53\u306b\u3042\u308a\u307e\u3059\uff0e<\/p>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0071635408\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000x = a \u306b\u304a\u3051\u308b f(x) \u306e\u30c6\u30fc\u30e9\u30fc\u7d1a\u6570\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e (a) \u3053\u3053\u3067 , x0 \u306f a \u3068 x \u306e\u7bc4\u56f2\u5185(b) \u306f reminder \u3068\u547c\u3070\u308c\uff0c f(x) \u304c\u6700\u4f4e\u3067\u3082 n \u6b21\u306e\u5fae\u5206\u4fc2\u6570\u3092\u6301\u3064\u3068\u60f3\u5b9a &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4367\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u30c6\u30fc\u30e9\u30fc\u7d1a\u6570&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4367","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4367"}],"version-history":[{"count":6,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4367\/revisions"}],"predecessor-version":[{"id":6806,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4367\/revisions\/6806"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}