{"id":6832,"date":"2021-10-21T19:32:39","date_gmt":"2021-10-21T14:02:39","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6832"},"modified":"2021-10-25T00:29:42","modified_gmt":"2021-10-24T18:59:42","slug":"evaluate-displaystylelim_x-to-infty-7x21over-5x2-1x5over-1-x3","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-infty-7x21over-5x2-1x5over-1-x3\/","title":{"rendered":"Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Here f(x) = \\({7x^2+1\\over 5x^2-1}\\)<\/p>\n<p>\\(\\phi\\)(x) = \\({x^5\\over {1-x^3}}\\) = \\(x^2x^3\\over 1-x^3\\) = \\(x^2\\over {1\\over x^3}-1\\)<\/p>\n<p>\\(\\therefore\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) f(x) = \\(7\\over 5\\) &amp;amp;\u00a0 \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(\\phi\\)(x) \\(\\rightarrow\\) &#8211; \\(\\infty\\)<\/p>\n<p>\\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\((f(x))^{\\phi (x)}\\) = \\(({7\\over 5})^{-\\infty}\\) = 0<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-0-x3-cotxover-1-cosx\/\" aria-label=\"\u201cEvaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\)\u201d (Edit)\">Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/\" aria-label=\"\u201cEvaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x \u2013 5}\\)\u201d (Edit)\">Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x \u2013 5}\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-0-xln12tanxover-1-cosx\/\" aria-label=\"\u201cEvaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(xln(1+2tanx)\\over 1-cosx\\)\u201d (Edit)\">Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(xln(1+2tanx)\\over 1-cosx\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-0-2xsin2x-2sin2over-x\/\" aria-label=\"\u201cEvaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\((2+x)sin(2+x)-2sin2\\over x\\)\u201d (Edit)\">Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\((2+x)sin(2+x)-2sin2\\over x\\)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-displaystylelim_x-to-inftyx31over-x21-axb-2-then-find-the-value-of-a-and-b\/\" aria-label=\"\u201cIf \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2, then find the value of a and b.\u201d (Edit)\">If \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2, then find the value of a and b.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Here f(x) = \\({7x^2+1\\over 5x^2-1}\\) \\(\\phi\\)(x) = \\({x^5\\over {1-x^3}}\\) = \\(x^2x^3\\over 1-x^3\\) = \\(x^2\\over {1\\over x^3}-1\\) \\(\\therefore\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) f(x) = \\(7\\over 5\\) &amp;amp;\u00a0 \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(\\phi\\)(x) \\(\\rightarrow\\) &#8211; \\(\\infty\\) \\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\((f(x))^{\\phi (x)}\\) = \\(({7\\over 5})^{-\\infty}\\) = 0 Similar Questions Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\) &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-infty-7x21over-5x2-1x5over-1-x3\/\"> <span class=\"screen-reader-text\">Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[54,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-infty-7x21over-5x2-1x5over-1-x3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : Here f(x) = ({7x^2+1over 5x^2-1}) (phi)(x) = ({x^5over {1-x^3}}) = (x^2x^3over 1-x^3) = (x^2over {1over x^3}-1) (therefore) (displaystyle{lim_{x to infty}}) f(x) = (7over 5) &amp;amp;\u00a0 (displaystyle{lim_{x to infty}}) (phi)(x) (rightarrow) &#8211; (infty) (implies) (displaystyle{lim_{x to infty}}) ((f(x))^{phi (x)}) = (({7over 5})^{-infty}) = 0 Similar Questions Evaluate : (displaystyle{lim_{x to 0}}) (x^3 cotxover {1-cosx}) &hellip; Evaluate : (displaystyle{lim_{x to infty}}) (({7x^2+1over 5x^2-1})^{x^5over {1-x^3}}) Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-infty-7x21over-5x2-1x5over-1-x3\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T14:02:39+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T18:59:42+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" 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