{"id":143605,"date":"2024-09-23T21:49:10","date_gmt":"2024-09-23T21:49:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=143605"},"modified":"2024-09-23T21:49:12","modified_gmt":"2024-09-23T21:49:12","slug":"review-the-table-of-values-for-function-gx","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/23\/review-the-table-of-values-for-function-gx\/","title":{"rendered":"Review the table of values for function g(x)"},"content":{"rendered":"\n<p>Review the table of values for function g(x).<br>x<\/p>\n\n\n\n<p>g(x)<\/p>\n\n\n\n<p>28.9<\/p>\n\n\n\n<p>\u20133.751<\/p>\n\n\n\n<p>28.99<\/p>\n\n\n\n<p>\u20133.76<\/p>\n\n\n\n<p>28.999<\/p>\n\n\n\n<p>\u20133.9<\/p>\n\n\n\n<p>29<\/p>\n\n\n\n<p>undefined<\/p>\n\n\n\n<p>29.001<\/p>\n\n\n\n<p>\u20134.1<\/p>\n\n\n\n<p>29.01<\/p>\n\n\n\n<p>\u20134.24<\/p>\n\n\n\n<p>29.1<\/p>\n\n\n\n<p>\u20134.249<\/p>\n\n\n\n<p>What is Limit of g (x) as x approaches 29g(x), if it exists?<\/p>\n\n\n\n<p>\u20134.25<br>\u20134<br>\u20133.75<br>DNE<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>\u20134<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find the limit of g(x)g(x)g(x) as xxx approaches 29, we need to evaluate the behavior of the function from both sides of x=29x = 29x=29. Limits help us understand the value that a function approaches as the input xxx gets closer and closer to a particular point, even if the function is not defined at that point.<\/p>\n\n\n\n<p>In this case, we are given the following values for g(x)g(x)g(x):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>As xxx approaches 29 from the left:\n<ul class=\"wp-block-list\">\n<li>At x=28.9x = 28.9x=28.9, g(x)=\u22123.751g(x) = -3.751g(x)=\u22123.751.<\/li>\n\n\n\n<li>At x=28.99x = 28.99x=28.99, g(x)=\u22123.76g(x) = -3.76g(x)=\u22123.76.<\/li>\n\n\n\n<li>At x=28.999x = 28.999x=28.999, g(x)=\u22123.9g(x) = -3.9g(x)=\u22123.9.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>As xxx approaches 29 from the right:\n<ul class=\"wp-block-list\">\n<li>At x=29.001x = 29.001x=29.001, g(x)=\u22124.1g(x) = -4.1g(x)=\u22124.1.<\/li>\n\n\n\n<li>At x=29.01x = 29.01x=29.01, g(x)=\u22124.24g(x) = -4.24g(x)=\u22124.24.<\/li>\n\n\n\n<li>At x=29.1x = 29.1x=29.1, g(x)=\u22124.249g(x) = -4.249g(x)=\u22124.249.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>We also know that g(x)g(x)g(x) is undefined at exactly x=29x = 29x=29, but that doesn&#8217;t prevent the limit from existing. What we are interested in is whether the values of g(x)g(x)g(x) approach a single number as xxx gets closer to 29 from both sides.<\/p>\n\n\n\n<p>From the left-hand side (x\u219229\u2212x \\to 29^-x\u219229\u2212), the values of g(x)g(x)g(x) are getting closer to approximately \u22124-4\u22124. From the right-hand side (x\u219229+x \\to 29^+x\u219229+), the values of g(x)g(x)g(x) are also getting closer to \u22124-4\u22124.<\/p>\n\n\n\n<p>Since the function approaches \u22124-4\u22124 from both directions, we conclude that the limit of g(x)g(x)g(x) as xxx approaches 29 is:lim\u2061x\u219229g(x)=\u22124\\lim_{{x \\to 29}} g(x) = -4x\u219229lim\u200bg(x)=\u22124<\/p>\n\n\n\n<p>The limit exists and is equal to \u22124-4\u22124, even though the function is undefined at x=29x = 29x=29. This demonstrates how limits can describe the behavior of a function near a point, even when the function has no value at that point.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Review the table of values for function g(x).x g(x) 28.9 \u20133.751 28.99 \u20133.76 28.999 \u20133.9 29 undefined 29.001 \u20134.1 29.01 \u20134.24 29.1 \u20134.249 What is Limit of g (x) as x approaches 29g(x), if it exists? \u20134.25\u20134\u20133.75DNE The Correct answer and Explanation is: The correct answer is \u20134. Explanation: To find the limit of g(x)g(x)g(x) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-143605","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143605","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=143605"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/143605\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=143605"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=143605"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=143605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}