{"id":2112,"date":"2022-02-22T14:05:43","date_gmt":"2022-02-22T05:05:43","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2112"},"modified":"2024-04-26T17:31:43","modified_gmt":"2024-04-26T08:31:43","slug":"%e5%8f%82%e8%80%83%ef%bc%9a%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e6%a5%b5%e9%99%90%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a8%bc%e6%98%8e","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e6%a5%b5%e9%99%90%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a8%bc%e6%98%8e\/","title":{"rendered":"\u53c2\u8003\uff1a\u4e09\u89d2\u95a2\u6570\u306e\u6975\u9650\u516c\u5f0f\u306e\u8a3c\u660e"},"content":{"rendered":"<p>\\(\\displaystyle \\lim_{x \\rightarrow 0} \\frac{\\sin x}{x} = 1\\) \u306e\u8a3c\u660e\u3002\u3053\u308c\u3092\u4f7f\u3063\u3066\u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206\u3092\u5c0e\u304f\u306e\u3067\u3042\u308b\u304b\u3089\uff0c\u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206\u3092\u524d\u63d0\u3068\u3057\u305f\u30ed\u30d4\u30bf\u30eb\u306e\u5b9a\u7406\u306a\u3069\u3092\u4f7f\u3063\u3066\u306f\u8a3c\u660e\u306b\u306a\u308a\u307e\u305b\u3093\u3088\u3002<br \/>\n<!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8493\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Limitfig1.svg\" alt=\"\" width=\"460\" height=\"345\" \/><\/p>\n<p>&nbsp;<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_1757\" dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8483\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/limitS.svg\" alt=\"\" width=\"460\" height=\"345\" \/>\u534a\u5f84 \\(r = 1\\)\uff08\u3064\u307e\u308a\uff0c\\(OA = OB = 1\\)\uff09\uff0c\u4e2d\u5fc3\u89d2 \\(x\\) \uff08\u30e9\u30b8\u30a2\u30f3\uff09\u306e\u6247\u5f62 \\(OAB\\) \u306e\u9762\u7a4d \\(\\color{red}{S}\\) \u306f\uff0c<br id=\"yui_3_17_2_1_1645505207625_1766\" \/>$$\\color{red}{S = \\frac{x}{2}}$$\u3053\u308c\u306f\uff0c\u6247\u5f62\u306e\u9762\u7a4d\u304c\u4e2d\u5fc3\u89d2\u306b\u6bd4\u4f8b\u3057\uff0c\u7279\u306b \\(x = 2 \\pi \\) \u306e\u3068\u304d \\(S = \\pi r^2 = \\pi, (\\because \\ r = 1)\\) \u3068\u306a\u308b\u3053\u3068\u304b\u3089\u308f\u304b\u308b\u3002<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8484\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/limitS1.svg\" alt=\"\" width=\"460\" height=\"345\" \/><\/p>\n<p>\u6b21\u306b\uff0c\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62 \\(OAB\\) \u306e\u9762\u7a4d \\(\\color{darkgreen}{S_1}\\) \u306f\uff0c\u5e95\u8fba\u304c \\(OA = 1, \\) \u9ad8\u3055\u304c \\(PB = \\sin x\\) \u3067\u3042\u308b\u3053\u3068\u304b\u3089<br id=\"yui_3_17_2_1_1645505207625_1976\" \/>$$\\color{darkgreen}{S_1 = \\frac{1}{2} \\sin x}$$<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8485\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/limitS2.svg\" alt=\"\" width=\"460\" height=\"345\" \/><\/p>\n<p id=\"yui_3_17_2_1_1645505207625_2186\" dir=\"ltr\">\u307e\u305f\uff0c\u76f4\u89d2\u4e09\u89d2\u5f62 \\(OAC\\) \u306e\u9762\u7a4d \\(\\color{blue}{S_2}\\) \u306f\uff0c\u5e95\u8fba\u304c \\(OA = 1, \\) \u9ad8\u3055\u304c \\(AC = \\tan x\\) \u3067\u3042\u308b\u3053\u3068\u304b\u3089<br id=\"yui_3_17_2_1_1645505207625_2204\" \/>$$ \\color{blue}{S_2 = \\frac{1}{2} \\tan x}$$<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-8481\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/limitfig1a.svg\" alt=\"\" width=\"460\" height=\"345\" \/><\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-8514\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/LimitSall.svg\" alt=\"\" width=\"640\" height=\"286\" \/><\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3030\" dir=\"ltr\">\u56f3\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\uff0c<br id=\"yui_3_17_2_1_1645505207625_3100\" \/>$$ {\\color{darkgreen}{S_1}} &lt; {\\color{red}{S}} &lt; {\\color{blue}{S_2}}$$ \u3067\u3042\u308b\u304b\u3089<br id=\"yui_3_17_2_1_1645505207625_3101\" \/>$$ {\\color{darkgreen}{\\frac{1}{2} \\sin x}} &lt; {\\color{red}{\\frac{x}{2}}} &lt; {\\color{blue}{\\frac{1}{2} \\tan x }}$$<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3102\" dir=\"ltr\">\\( \\sin x &gt; 0 \\) \u3068\u3057\u3066\u5404\u9805\u306b \\(\\displaystyle \\frac{2}{\\sin x}\\) \u3092\u304b\u3051\u3066&#8230;<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3104\" dir=\"ltr\">$$ 1 &lt; \\frac{x}{\\sin x} &lt; \\frac{1}{\\cos x}$$<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3105\" dir=\"ltr\">\u9006\u6570\u3092\u3068\u308b\u3068\u4e0d\u7b49\u53f7\u306e\u5411\u304d\u304c\u304b\u308f\u308a&#8230;<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3106\" dir=\"ltr\">$$\\therefore \\ 1 &gt; \\frac{\\sin x}{x} &gt; \\cos x$$<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3107\" dir=\"ltr\">\u5404\u9805\u306e\u6975\u9650\u3092\u3068\u308b\u3068&#8230;<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3109\" dir=\"ltr\">$$ \\lim_{x \\rightarrow 0} 1 = 1 \\geq \\lim_{x \\rightarrow 0}\\frac{\\sin x}{x} \\geq \\lim_{x \\rightarrow 0}\\cos x = 1$$<\/p>\n<p dir=\"ltr\">\u3064\u307e\u308a\uff0c<\/p>\n<p dir=\"ltr\">$$ 1 \\geq \\lim_{x \\rightarrow 0}\\frac{\\sin x}{x} \\geq 1$$<\/p>\n<p id=\"yui_3_17_2_1_1645505207625_3059\" dir=\"ltr\">$$\\therefore \\ \\lim_{x \\rightarrow 0}\\frac{\\sin x}{x} = 1$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\\(\\displaystyle \\lim_{x \\rightarrow 0} \\frac{\\sin x}{x} = 1\\) \u306e\u8a3c\u660e\u3002\u3053\u308c\u3092\u4f7f\u3063\u3066\u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206\u3092\u5c0e\u304f\u306e\u3067\u3042\u308b\u304b\u3089\uff0c\u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206\u3092\u524d\u63d0\u3068\u3057\u305f\u30ed\u30d4\u30bf\u30eb\u306e\u5b9a\u7406\u306a\u3069\u3092\u4f7f\u3063\u3066\u306f\u8a3c\u660e\u306b\u306a\u308a\u307e\u305b\u3093\u3088\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e6%a5%b5%e9%99%90%e5%85%ac%e5%bc%8f%e3%81%ae%e8%a8%bc%e6%98%8e\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2096,"menu_order":30,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2112","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"\\(\\displaystyle \\lim_{x \\rightarrow 0} \\frac{\\sin x}{x}\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" 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