{"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":"

Solution :<\/h2>\n

Here f(x) = \\({7x^2+1\\over 5x^2-1}\\)<\/p>\n

\\(\\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

\\(\\therefore\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) f(x) = \\(7\\over 5\\) &amp;\u00a0 \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(\\phi\\)(x) \\(\\rightarrow\\) – \\(\\infty\\)<\/p>\n

\\(\\implies\\) \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\((f(x))^{\\phi (x)}\\) = \\(({7\\over 5})^{-\\infty}\\) = 0<\/p>\n


\n

Similar Questions<\/h3>\n

Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\)<\/a><\/p>\n

Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x \u2013 5}\\)<\/a><\/p>\n

Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(xln(1+2tanx)\\over 1-cosx\\)<\/a><\/p>\n

Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\((2+x)sin(2+x)-2sin2\\over x\\)<\/a><\/p>\n

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":"

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;\u00a0 \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(\\phi\\)(x) \\(\\rightarrow\\) – \\(\\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}\\) …<\/p>\n

Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)<\/span> Read More »<\/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":"\nEvaluate : \\(\\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, 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