{"id":7189,"date":"2021-10-23T00:18:33","date_gmt":"2021-10-22T18:48:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7189"},"modified":"2021-10-25T00:29:36","modified_gmt":"2021-10-24T18:59:36","slug":"evaluate-displaystylelim_x-to-0-x3-cotxover-1-cosx","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-0-x3-cotxover-1-cosx\/","title":{"rendered":"Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\)"},"content":{"rendered":"

Solution :<\/h2>\n

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

= \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cosx(1 + cosx)\\over {sinxsin^2x}\\)<\/p>\n

= \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\({x^3\\over sin^3x}.cosx(1 + cosx)\\) = 2<\/p>\n

\n

Similar Questions<\/h3>\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 \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\)<\/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 : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cosx\\over {sinx(1-cosx)}\\) = \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cosx(1 + cosx)\\over {sinxsin^2x}\\) = \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\({x^3\\over sin^3x}.cosx(1 + cosx)\\) = 2 Similar Questions Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(x^2 + x + 1\\over {3x^2 + 2x \u2013 5}\\) Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\) Evaluate …<\/p>\n

Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\)<\/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 0}}\\) \\(x^3 cotx\\over {1-cosx}\\)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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