{"id":9931,"date":"2022-02-03T15:13:42","date_gmt":"2022-02-03T09:43:42","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9931"},"modified":"2022-02-03T18:31:39","modified_gmt":"2022-02-03T13:01:39","slug":"rationalisation-method-to-solve-limits","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/rationalisation-method-to-solve-limits\/","title":{"rendered":"Rationalisation Method to Solve Limits"},"content":{"rendered":"

Here you will learn what is the rationalisation method to solve or find limits with examples.<\/p>\n

Let’s begin –<\/p>\n

Rationalisation Method to Solve Limits<\/h2>\n

This method is particularly used when either the numerator or denominator or both involve expression consisting of square roots and substituting the value of x the rational expression takes the form \\(0\\over 0\\), \\(\\infty\\over \\infty\\).<\/p>\n

Also Read : How to Solve Indeterminate Forms of Limits<\/a><\/p>\n

Following examples illustrate the above method :<\/p>\n

Example<\/strong><\/span> : Evaluate : \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(\\sqrt{2 + x} – \\sqrt{2}\\over x\\).<\/p>\n

Solution<\/strong><\/span> : When x = 0, the expression \\(\\sqrt{2 + x} – \\sqrt{2}\\over x\\) takes the form \\(0\\over 0\\).<\/p>\n

Rationalising the numerator we have,<\/p>\n

\\(\\displaystyle{\\lim_{x \\to 0}}\\) \\((\\sqrt{2 + x} – \\sqrt{2})(\\sqrt{2 + x} + \\sqrt{2})\\over x(\\sqrt{2 + x} + \\sqrt{2})\\)<\/p>\n

= \\(\\displaystyle{\\lim_{x \\to 0}}\\) \\(2 + x – 2\\over x(\\sqrt{2 + x} + \\sqrt{2})\\)<\/p>\n

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

Example<\/strong><\/span> : Evaluate the limit : \\(\\displaystyle{\\lim_{x \\to 1}}\\) [\\({4 – \\sqrt{15x + 1}}\\over {2 – \\sqrt{3x + 1}}\\)]<\/p>\n

Solution<\/strong><\/span> : \\(\\displaystyle{\\lim_{x \\to 1}}\\) [\\({4 – \\sqrt{15x + 1}}\\over {2 – \\sqrt{3x + 1}}\\)]<\/p>\n

Rationalising the numerator and denominator both we have,<\/p>\n

= \\(\\displaystyle{\\lim_{x \\to 1}}\\) \\({(4 – \\sqrt{15x + 1})(2 + \\sqrt{3x + 1})(4 + \\sqrt{15x + 1})}\\over {(2 – \\sqrt{3x + 1})(4 + \\sqrt{15x + 1})(2 + \\sqrt{3x + 1})}\\)<\/p>\n

= \\(\\displaystyle{\\lim_{x \\to 1}}\\) \\((15 – 15x)\\over {3 – 3x}\\)\\(\\times\\)\\(2 + \\sqrt{3x + 1}\\over {4 + \\sqrt{15x + 1}}\\)<\/p>\n

= \\(5\\over 2\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the rationalisation method to solve or find limits with examples. Let’s begin – Rationalisation Method to Solve Limits This method is particularly used when either the numerator or denominator or both involve expression consisting of square roots and substituting the value of x the rational expression takes the form …<\/p>\n

Rationalisation Method to Solve Limits<\/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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[19],"tags":[],"yoast_head":"\nRationalisation Method to Solve Limits - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the rationalisation method to solve or find limits with examples.\" \/>\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\/rationalisation-method-to-solve-limits\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rationalisation Method to Solve Limits - 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