{"id":6825,"date":"2021-10-21T19:22:50","date_gmt":"2021-10-21T13:52:50","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6825"},"modified":"2021-10-25T00:29:58","modified_gmt":"2021-10-24T18:59:58","slug":"if-displaystylelim_x-to-inftyx31over-x21-axb-2-then-find-the-value-of-a-and-b","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-displaystylelim_x-to-inftyx31over-x21-axb-2-then-find-the-value-of-a-and-b\/","title":{"rendered":"If \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2, then find the value of a and b."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>\\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2<\/p>\n<p>\\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)\\(x^3(1-a)-bx^2-ax+(1-b)\\over x^2+1\\) = 2<\/p>\n<p>\\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)\\(x(1-a)-b-{a\\over x}+{(1-b)\\over x^2}\\over 1+{1\\over x^2}\\) = 2<\/p>\n<p>\\(\\implies\\) 1 &#8211; a = 0, -b = 2 \\(\\implies\\) a = 1, b = -2<\/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\/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","protected":false},"excerpt":{"rendered":"<p>Solution : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2 \\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)\\(x^3(1-a)-bx^2-ax+(1-b)\\over x^2+1\\) = 2 \\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)\\(x(1-a)-b-{a\\over x}+{(1-b)\\over x^2}\\over 1+{1\\over x^2}\\) = 2 \\(\\implies\\) 1 &#8211; a = 0, -b = 2 \\(\\implies\\) a = 1, b = -2 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\/if-displaystylelim_x-to-inftyx31over-x21-axb-2-then-find-the-value-of-a-and-b\/\"> <span class=\"screen-reader-text\">If \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2, then find the value of a and b.<\/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>If \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2, then find the value of a and b.<\/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\/if-displaystylelim_x-to-inftyx31over-x21-axb-2-then-find-the-value-of-a-and-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If \\(\\displaystyle{\\lim_{x \\to \\infty}}\\)(\\({x^3+1\\over x^2+1}-(ax+b)\\)) = 2, then find the value of a and b.\" \/>\n<meta property=\"og:description\" content=\"Solution : (displaystyle{lim_{x to infty}})(({x^3+1over x^2+1}-(ax+b))) = 2 (implies) (displaystyle{lim_{x to infty}})(x^3(1-a)-bx^2-ax+(1-b)over x^2+1) = 2 (implies) (displaystyle{lim_{x to infty}})(x(1-a)-b-{aover x}+{(1-b)over x^2}over 1+{1over x^2}) = 2 (implies) 1 &#8211; a = 0, -b = 2 (implies) a = 1, b = -2 Similar Questions Evaluate : (displaystyle{lim_{x to 0}}) (x^3 cotxover {1-cosx}) Evaluate : (displaystyle{lim_{x to &hellip; If (displaystyle{lim_{x to infty}})(({x^3+1over x^2+1}-(ax+b))) = 2, then find the value of a and b. 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