{"id":7191,"date":"2021-10-23T00:20:44","date_gmt":"2021-10-22T18:50:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7191"},"modified":"2021-10-25T00:27:30","modified_gmt":"2021-10-24T18:57:30","slug":"evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/","title":{"rendered":"Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x &#8211; 5}\\)"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>\\(\\displaystyle{\\lim_{x \\to \\infty}}\\)\\(x^2 + x + 1\\over {3x^2 + 2x &#8211; 5}\\)<\/p>\n<p>It is (\\(\\infty\\over \\infty\\) form),\u00a0 \u00a0Put x = \\(1\\over y\\)<\/p>\n<p>= \\(\\displaystyle{\\lim_{y \\to 0}}\\) \\(1 + y + y^2\\over {3 + 2y &#8211; 5y^2}\\) = \\(1\\over 3\\)<\/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-displaystylelim_x-to-infty-7x21over-5x2-1x5over-1-x3\/\" aria-label=\"\u201cEvaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)\u201d (Edit)\">Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)<\/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\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)\\(x^2 + x + 1\\over {3x^2 + 2x &#8211; 5}\\) It is (\\(\\infty\\over \\infty\\) form),\u00a0 \u00a0Put x = \\(1\\over y\\) = \\(\\displaystyle{\\lim_{y \\to 0}}\\) \\(1 + y + y^2\\over {3 + 2y &#8211; 5y^2}\\) = \\(1\\over 3\\) Similar Questions Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\) Evaluate : \\(\\displaystyle{\\lim_{x \\to &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/\"> <span class=\"screen-reader-text\">Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x &#8211; 5}\\)<\/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 the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x - 5}\\)<\/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-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x - 5}\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : (displaystyle{lim_{x to infty}})(x^2 + x + 1over {3x^2 + 2x &#8211; 5}) It is ((inftyover infty) form),\u00a0 \u00a0Put x = (1over y) = (displaystyle{lim_{y to 0}}) (1 + y + y^2over {3 + 2y &#8211; 5y^2}) = (1over 3) Similar Questions Evaluate : (displaystyle{lim_{x to 0}}) (x^3 cotxover {1-cosx}) Evaluate : (displaystyle{lim_{x to &hellip; Evaluate the limit : (displaystyle{lim_{x to infty}}) (x^2 + x + 1over {3x^2 + 2x &#8211; 5}) Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T18:50:44+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T18:57:30+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\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Evaluate the limit : \\\\(\\\\displaystyle{\\\\lim_{x \\\\to \\\\infty}}\\\\) \\\\(x^2 + x + 1\\\\over {3x^2 + 2x &#8211; 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5}) It is ((inftyover infty) form),\u00a0 \u00a0Put x = (1over y) = (displaystyle{lim_{y to 0}}) (1 + y + y^2over {3 + 2y &#8211; 5y^2}) = (1over 3) Similar Questions Evaluate : (displaystyle{lim_{x to 0}}) (x^3 cotxover {1-cosx}) Evaluate : (displaystyle{lim_{x to &hellip; Evaluate the limit : (displaystyle{lim_{x to infty}}) (x^2 + x + 1over {3x^2 + 2x &#8211; 5}) Read More &raquo;","og_url":"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T18:50:44+00:00","article_modified_time":"2021-10-24T18:57:30+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/evaluate-the-limit-displaystylelim_x-to-infty-x2-x-1over-3x2-2x-5\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x &#8211; 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