\u3000\u8aac\u660e\u3092\u3057\u306a\u304c\u3089\u89e3\u3044\u3066\u3044\u304f\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n
(1) \\(x\\to\\infty\\) \u306e\u3068\u304d \\(\\sqrt{x^{2}+4x+2}\\to\\infty\\),\u3000\\(\\sqrt{x^{2}-2x+5}\\to \\infty\\) \u3067\u3042\u308b\u306e\u3067, \u554f\u984c\u6587\u306e\u6975\u9650\u306f\u300c\\(\\infty -\\infty\\) \u578b\u306e\u4e0d\u5b9a\u5f62\u300d\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066, \u9069\u5207\u306a\u5909\u5f62\u3092\u3057\u3066\u4e0d\u5b9a\u5f62\u3067\u306f\u306a\u3044\u5f62\u306b\u5909\u5f62\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u305d\u308c\u306f, \u3053\u306e\u5834\u5408\u306f\u300c\u5206\u5b50\u306e\u6709\u7406\u5316\u300d\u3068\u3044\u3046\u64cd\u4f5c\u3092\u884c\u306a\u3044\u307e\u3059\u3002
\n\u3000\u6b21\u306e\u3088\u3046\u306b\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n
\u3000\u3000\\(\\begin{align}
\n\\displaystyle\\lim_{x\\to\\infty}(\\sqrt{x^{2}+4x+2}-\\sqrt{x^{2}-2x+5})&=\\displaystyle\\lim_{x\\to\\infty}\\frac{(x^{2}+4x+2)-(x^{2}-2x+5)}{\\sqrt{x^{2}+4x+2}+\\sqrt{x^{2}-2x+5}}\\\\
\n\u3000\u3000\u3000\u3000&=\\displaystyle\\lim_{x\\to\\infty}\\frac{6x-3}{\\sqrt{x^{2}+4x+2}+\\sqrt{x^{2}-2x+5}}\\\\
\n\u3000\u3000\u3000\u3000&=\\displaystyle\\lim_{x\\to\\infty}\\frac{6-\\displaystyle\\frac{3}{\\,x\\,}}{\\sqrt{1+\\displaystyle\\frac{4}{\\,x\\,}+\\frac{2}{\\,x^{2}\\,}} +\\sqrt{1-\\displaystyle\\frac{2}{\\,x\\,}+\\frac{5}{\\,x^{2}}\\,}}\\\\
\n\u3000\u3000\u3000\u3000&=\\displaystyle\\frac{6}{1+1}\\\\
\n\u3000\u3000\u3000\u3000&=3\u3000\u3000(\u7b54)\\\\
\n\\end{align}\\)
\n\u3000
\n(2) (1) \u3067\u306f\u300c\u5206\u5b50\u306e\u6709\u7406\u5316\u300d\u3092\u884c\u306a\u3044\u307e\u3057\u305f\u304c, \u3053\u306e\u554f\u984c\u306e\u5834\u5408\u306f\u305d\u308c\u3092\u884c\u306a\u3046\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6b21\u306e\u3088\u3046\u306b\u89e3\u3051\u3070\u3088\u3044\u306e\u3067\u3059\u3002<\/p>\n
\u3000\u3000\\(\\begin{align} \u3068\u8003\u3048\u307e\u3059\u3002\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n \u3000\\(\\displaystyle\\lim_{x\\to\\infty}(\\sqrt{3x+1}-\\sqrt{x+2})(\\sqrt{2x+5}-\\sqrt{2x-1})\\) \u3000\u8aac\u660e\u3092\u3057\u306a\u304c\u3089\u89e3\u3044\u3066\u3044\u304f\u3053\u3068\u306b\u3057\u307e\u3059\u3002 (1) \\(x\\to\\infty\\) \u306e\u3068\u304d \\(\\sqrt{x^{2}+4x+2}\\to\\infty\\),\u3000\\(\\sqrt{x^{2}-2x+5}\\to \\infty\\) \u3067\u3042 […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[21],"class_list":["post-1504","post","type-post","status-publish","format-standard","hentry","category-11","tag-etude-knowledge"],"_links":{"self":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1504","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1504"}],"version-history":[{"count":4,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1504\/revisions"}],"predecessor-version":[{"id":1508,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1504\/revisions\/1508"}],"wp:attachment":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\\displaystyle\\lim_{x\\to\\infty}(\\sqrt{2x^{2}+4x+3}-\\sqrt{x^{2}+2x+9})&=\\displaystyle\\lim_{x\\to\\infty}x\\left( \\sqrt{2+\\displaystyle\\frac{4}{\\,x\\,}+\\frac{3}{\\,x^{2}\\,}}-\\sqrt{1+\\displaystyle\\frac{2}{x}+\\frac{9}{x^{2}}}\\right)\\\\
\n\u3000\u3000\u3000\u3000&=\\infty\u3000\u3000\u3000(\u7b54)\\\\
\n\\end{align}\\)
\n\u3000
\n\u3000\u7b54\u306e\u4e00\u3064\u524d\u306e\u5f0f\u3067\u306f, (\u3000) \u5185\u306f \\(\\sqrt{2}-1\\) \u306b\u8fd1\u3065\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066, \u3053\u306e\u6975\u9650\u306f, \u300c\\(\\infty\\times (\\sqrt{2}-1)\\)\u300d\u578b\u306e\u6975\u9650\u3067\u3059\u306e\u3067, \u7d50\u679c\u306f \\(\\infty\\) \u306b\u306a\u308a\u307e\u3059\u3002
\n\u3000(2) \u306f (1) \u306e\u3088\u3046\u306b\u300c\u6709\u7406\u5316\u300d\u3092\u884c\u306a\u3063\u3066\u3082\u6975\u9650\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u3067\u304d\u308b\u306e\u3067\u3059\u304c, \u300c\u308f\u3056\u308f\u3056\u300d\u305d\u308c\u3092\u884c\u306a\u308f\u306a\u304b\u3063\u305f\u306e\u306f, \u6839\u53f7\u5185\u306e\u6700\u9ad8\u6b21\u306e\u4fc2\u6570\u304c\u7570\u306a\u3063\u3066\u3044\u308b\u304b\u3089<\/strong>\u3068\u3044\u3046\u306e\u304c\u7406\u7531\u3067\u3059\u3002\u3082\u3046\u5c11\u3057\u8a73\u3057\u304f\u8aac\u660e\u3059\u308b\u3068, \\(\\sqrt{2x^{2}+4x+3}\\) \u306f\u304a\u3088\u305d \\(\\sqrt{2}x\\) \u7a0b\u5ea6\u306e\u901f\u3055\u3067\u5927\u304d\u304f\u306a\u308b\u306e\u306b\u5bfe\u3057, \\(\\sqrt{x^{2}+2x+9}\\) \u306f \\(x\\) \u7a0b\u5ea6\u306e\u901f\u3055\u3067\u5927\u304d\u304f\u306a\u308b\u306e\u3067, \\(x\\) \u304c\u5927\u304d\u304f\u306a\u308b\u3068\u5dee\u304c\u5e83\u304c\u3063\u3066\u3044\u304f\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002\u3064\u307e\u308a, (2) \u306f\u898b\u305f\u76ee\u3067\u3082\u6975\u9650\u306f\u3042\u308b\u7a0b\u5ea6\u4e88\u60f3\u3067\u304d\u308b\u3088\u3046\u306a\u3082\u306e\u3067, \u300c\u308f\u3056\u308f\u3056\u300d\u6709\u7406\u5316\u307e\u3067\u3057\u306a\u304f\u3066\u3082\u308f\u304b\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002
\n\u3000\u3053\u3053\u307e\u3067\u3092\u3082\u3046\u4e00\u5ea6\u632f\u308a\u8fd4\u308b\u3068,
\n\u3000
\n\u3000(1) \u3067\u306f, \\(\\sqrt{x^{2}+4x+2}\\) \u3068 \\(\\sqrt{x^{2}-2x+5}\\) \u306e \\(x^{2}\\) \u306e\u4fc2\u6570\u306f\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u3068\u304d\u306b\u6709\u7406\u5316\u3092\u884c\u306a\u3044\u307e\u3059\u3002
\n\u3000(2) \u3067\u306f \\(\\sqrt{2x^{2}+4x+3}\\) \u3068 \\(\\sqrt{x^{2}+4x+9}\\) \u306e \\(x^{2}\\) \u306e\u4fc2\u6570\u304c\u7570\u306a\u308b\u306e\u3067, \u3053\u306e\u3088\u3046\u306a\u5834\u5408\u306f\u6709\u7406\u5316\u3092\u3057\u306a\u304f\u3066\u3082\u7b54\u306f\u3059\u3050\u306b\u308f\u304b\u308a\u307e\u3059\u3002
\n\u3000
\n\u3000\u3053\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002
\n\u3000
\n(3)\u3000(2) \u3067\u306e\u8aac\u660e\u3092\u3075\u307e\u3048\u308b\u3068, \u6975\u9650\u3092\u69cb\u6210\u3057\u3066\u3044\u308b 2 \u3064\u306e\u5dee\u306e\u3046\u3061, <\/p>\n\n
\n\u3000\\(\\begin{align}
\n\u3000\u3000&=\\displaystyle\\lim_{x\\to\\infty}(\\sqrt{3x+1}-\\sqrt{x+2})\\cdot \\displaystyle\\frac{(2x+5)-(2x-1)}{\\sqrt{2x+5}+\\sqrt{2x-1}}\\\\
\n\u3000\u3000&=\\displaystyle\\lim_{x\\to\\infty}\\displaystyle\\frac{6(\\sqrt{3x+1}-\\sqrt{x+2})}{\\sqrt{2x+5}+\\sqrt{2x-1}}\\\\
\n\u3000\u3000&=\\displaystyle\\lim_{x\\to\\infty}\\displaystyle\\frac{6\\left( \\sqrt{3+\\displaystyle\\frac{1}{\\,3\\,}}-\\sqrt{1+\\displaystyle\\frac{2}{\\,x\\,}}\\right)}{\\sqrt{2+\\displaystyle\\frac{5}{\\,x\\,}}+\\sqrt{2-\\displaystyle\\frac{1}{\\,x\\,}}}\\\\
\n\u3000\u3000&=\\displaystyle\\frac{6(\\sqrt{3}-1)}{2\\sqrt{2}}\\\\
\n\u3000\u3000&=\\displaystyle\\frac{3(\\sqrt{3}-1)}{\\sqrt{2}}\\\\
\n\u3000\u3000&=\\displaystyle\\frac{3}{\\,2\\,}(\\sqrt{6}-\\sqrt{2})\u3000\u3000\u3000(\u7b54)\\\\
\n\\end{align}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"