{"id":6827,"date":"2021-10-21T19:24:48","date_gmt":"2021-10-21T13:54:48","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6827"},"modified":"2021-10-25T00:29:53","modified_gmt":"2021-10-24T18:59:53","slug":"evaluate-displaystylelim_x-to-0-2xsin2x-2sin2over-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-0-2xsin2x-2sin2over-x\/","title":{"rendered":"Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\((2+x)sin(2+x)-2sin2\\over x\\)"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>\\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(2(sin(2+x)-sin2)+xsin(2+x)\\over x\\)<\/p>\n<p>= \\(\\displaystyle{\\lim_{x \\to 0}}\\)(\\(2.2.cos(2+{x\\over 2})sin{x\\over 2}\\over x\\) + sin(2+x))<\/p>\n<p>= \\(\\displaystyle{\\lim_{x \\to 0}}\\)\\(2cos(2+{x\\over 2})sin{x\\over 2}\\over {x\\over 2}\\) + \\(\\displaystyle{\\lim_{x \\to 0}}\\)sin(2+x)<\/p>\n<p>= 2cos2 + sin2<\/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-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\/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 : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(2(sin(2+x)-sin2)+xsin(2+x)\\over x\\) = \\(\\displaystyle{\\lim_{x \\to 0}}\\)(\\(2.2.cos(2+{x\\over 2})sin{x\\over 2}\\over x\\) + sin(2+x)) = \\(\\displaystyle{\\lim_{x \\to 0}}\\)\\(2cos(2+{x\\over 2})sin{x\\over 2}\\over {x\\over 2}\\) + \\(\\displaystyle{\\lim_{x \\to 0}}\\)sin(2+x) = 2cos2 + sin2 Similar Questions Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(x^3 cotx\\over {1-cosx}\\) Evaluate : \\(\\displaystyle{\\lim_{x \\to \\infty}}\\) \\(({7x^2+1\\over 5x^2-1})^{x^5\\over {1-x^3}}\\) Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/evaluate-displaystylelim_x-to-0-2xsin2x-2sin2over-x\/\"> <span class=\"screen-reader-text\">Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\((2+x)sin(2+x)-2sin2\\over x\\)<\/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 0}}\\) \\((2+x)sin(2+x)-2sin2\\over x\\)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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