{"id":9925,"date":"2022-02-03T14:37:10","date_gmt":"2022-02-03T09:07:10","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9925"},"modified":"2022-02-03T18:31:25","modified_gmt":"2022-02-03T13:01:25","slug":"direct-substitution-method-to-solve-limits","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/direct-substitution-method-to-solve-limits\/","title":{"rendered":"Direct Substitution Method to Solve Limits"},"content":{"rendered":"

Here you will learn direct substitution method to solve limits with examples.<\/p>\n

Let’s begin –<\/p>\n

Direct Substitution Method to Solve Limits<\/h2>\n

Consider the following limits :<\/p>\n

(i)  \\(lim_{x \\to a}\\) f(x)<\/p>\n

(ii)  \\(lim_{x \\to a} {\\phi(x)\\over \\psi(x)}\\)<\/p>\n

If f(a) and \\(\\phi(a)\\over \\psi(a)\\) exist and are fixed real numbers, then we say that<\/p>\n

\\(lim_{x \\to a}\\) f(x) = f(a)  and  \\(lim_{x \\to a} {\\phi(x)\\over \\psi(x)}\\) = \\(\\phi(a)\\over \\psi(a)\\)<\/p>\n

In other words, if the direct substitution of the point, to which the variable tends to, we obtain a fixed real number, then the number obtained is the limit of the function.<\/p>\n

Infact, if the point to which the variable tends to is a point in the domain of the function, then the value of the function at that point is its limit.<\/p>\n

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

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

Example<\/strong><\/span> : Evaluate : \\(lim_{x \\to 1}\\) \\(3x^2 + 4x + 5\\).<\/p>\n

Solution<\/strong><\/span> : We have,<\/p>\n

\\(lim_{x \\to 1}\\) \\(3x^2 + 4x + 5\\) = \\(3(1)^2 + 4(1) + 5\\) = 12.<\/p>\n

Example<\/strong><\/span> : Evaluate : \\(lim_{x \\to 2}\\) \\(x^2 – 4\\over x + 3\\).<\/p>\n

Solution<\/strong><\/span> : We have,<\/p>\n

\\(lim_{x \\to 2}\\) \\(x^2 – 4\\over x + 3\\) = \\(4 – 4\\over 2 + 3\\) = 0.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn direct substitution method to solve limits with examples. Let’s begin – Direct Substitution Method to Solve Limits Consider the following limits : (i)  \\(lim_{x \\to a}\\) f(x) (ii)  \\(lim_{x \\to a} {\\phi(x)\\over \\psi(x)}\\) If f(a) and \\(\\phi(a)\\over \\psi(a)\\) exist and are fixed real numbers, then we say that \\(lim_{x \\to a}\\) …<\/p>\n

Direct Substitution 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":"\nDirect Substitution Method to Solve Limits - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the direct substitution method to solve 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\/direct-substitution-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=\"Direct Substitution Method to Solve Limits - 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