{"id":731184,"date":"2024-08-29T16:24:18","date_gmt":"2024-08-29T10:54:18","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=731184"},"modified":"2024-08-29T16:24:18","modified_gmt":"2024-08-29T10:54:18","slug":"limits-in-maths","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/","title":{"rendered":"Limits in Maths"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Definition_in_Maths\" title=\"Limits Definition in Maths\">Limits Definition in Maths<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Definition_in_Calculus\" title=\"Limits Definition in Calculus\">Limits Definition in Calculus<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Types_of_Integrals\" title=\"Limits Types of Integrals\">Limits Types of Integrals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Definite_Integrals\" title=\"Definite Integrals\">Definite Integrals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Indefinite_Integrals\" title=\"Indefinite Integrals\">Indefinite Integrals<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_and_Functions\" title=\"Limits and Functions\">Limits and Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_and_Continuity\" title=\"Limits and Continuity\">Limits and Continuity<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_and_Derivatives\" title=\"Limits and Derivatives\">Limits and Derivatives<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Formulas\" title=\"Limits Formulas\">Limits Formulas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Formula_PDF\" title=\"Limits Formula PDF\">Limits Formula PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_of_Trigonometric_Functions\" title=\"Limits of Trigonometric Functions\">Limits of Trigonometric Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Properties\" title=\"Limits Properties\">Limits Properties<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Practice_Questions\" title=\"Limits Practice Questions\">Limits Practice Questions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#Limits_Maths_Practice_FAQs\" title=\"Limits Maths Practice FAQs\">Limits Maths Practice FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#What_is_a_limit_in_calculus\" title=\"What is a limit in calculus?\">What is a limit in calculus?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#How_do_you_find_the_limit_of_a_function_as_x_approaches_a_certain_value\" title=\"How do you find the limit of a function as x approaches a certain value?\">How do you find the limit of a function as x approaches a certain value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/limits-in-maths\/#What_does_it_mean_if_the_limit_does_not_exist\" title=\"What does it mean if the limit does not exist?\">What does it mean if the limit does not exist?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>In Maths, a limit is defined as a value that a function approaches for the given input. Limits are an important topic in mathematics. It is widely used in Calculus, for Mathematical analysis, to define integrals, derivatives, and continuity.<\/p>\n<p>This article will discuss the Limits in brief along with their types, formulas, and examples.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limits_Definition_in_Maths\"><\/span>Limits Definition in Maths<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For a real-valued function \u201cf\u201d and a real number \u201cc\u201d, the limit is defined as:<\/p>\n<p>lim<sub>x\u2192c<\/sub> f(x) = L<\/p>\n<p>This definition is read as \u201cthe limit of a function of x or \u201cf\u201d of x as x approaches c is equal to L.\u201d The word \u201clim\u201d represents limit as the right arrow defines that the function approaches the limit as x approaches c.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Limits_Definition_in_Calculus\"><\/span>Limits Definition in Calculus<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In calculus, we define a limit as a particular value to which the output of a function approaches the respective input value. It is used in analysis projects and hence, the limit is always concerned with the behavior of the function at a particular point.<\/p>\n<p>The representation of limits in calculus is as follows:<\/p>\n<p>lim<sub>x\u2192c<\/sub> f(x) = L<\/p>\n<p style=\"text-align: center;\"><strong>Also Check &#8211; <em><a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube\/\">Cube<\/a><\/em><\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Limits_Types_of_Integrals\"><\/span>Limits Types of Integrals<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Integrals are generally classified into two types. These are:<\/p>\n<ul>\n<li>Definite Integrals<\/li>\n<li>Indefinite Integrals<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Definite_Integrals\"><\/span>Definite Integrals<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Definite Integrals are defined as the integrals whose upper limit and lower limit are defined properly.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Indefinite_Integrals\"><\/span>Indefinite Integrals<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Indefinite Integrals are the integrals that are expressed without the upper and lower limits. The function will have an arbitrary constant that integrates it.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limits_and_Functions\"><\/span>Limits and Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A function may approach two different limits in some cases. These two approaches are:<\/p>\n<ul>\n<li>The first kind is when the variable approaches its limit through values that are larger than the limit. It is said to be a right-hand limit of the function.<\/li>\n<li>The second kind is when the variable approaches its limit through values that are smaller than the limit. It is said to be a left-hand limit of the function.<\/li>\n<\/ul>\n<p>In such cases, a limit is not defined.<\/p>\n<p>The limit of the function will exist if and only if both the right-hand limit and the left-hand limit are equal.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check &#8211; <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/fibonacci-sequence\/\"><span class=\"post post-post current-item\">Fibonacci Sequence<\/span><\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limits_and_Continuity\"><\/span>Limits and Continuity<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Limits and continuity are closely related concepts. A function can be either continuous or discontinuous. For a function to be continuous, small changes in the input should result in small changes in the output.<\/p>\n<p>If we say as f(x) \u2192 L as x \u2192 a, it means that the value of f(x) can get as close as we want to if x is close to a but is not equal to a.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limits_and_Derivatives\"><\/span>Limits and Derivatives<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To find the derivative of a function, f(a) or we can define it as a function at a point a, we use the following formula:<\/p>\n<p>f'(a) = lim<sub>x\u2192a<\/sub> (f(x) &#8211; f(a)) \/ (x &#8211; a)<\/p>\n<p>This formula helps us determine how the function changes at a point a.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limits_Formulas\"><\/span>Limits Formulas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Below is a list of the formulas used to solve the problem related to limits:<\/p>\n<ul>\n<li>lim<sub>x\u2192a<\/sub> (x<sup>n<\/sup> &#8211; a<sup>n<\/sup>) \/ (x-a) = na<sup>n-1<\/sup><\/li>\n<li>lim<sub>x\u21920<\/sub> (e<sup>x<\/sup> &#8211; 1) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (a<sup>x<\/sup> &#8211; 1) \/ x = ln a<\/li>\n<li>lim<sub>x\u21920<\/sub> (ln (1 + x)) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (log<sub>a<\/sub>(1 + x)) \/ x = log<sub>a<\/sub>e<\/li>\n<li>lim<sub>x\u21920<\/sub> (sin x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (tan x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (cos x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (sin<sup>-1<\/sup> x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (tan<sup>-1<\/sup> x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (1 + x)<sup>1\/x<\/sup> = e<\/li>\n<li>lim<sub>x\u2192\u221e<\/sub> (1 + 1\/x)<sup>x<\/sup> = e<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Limits_Formula_PDF\"><\/span>Limits Formula PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The formula sheets for Limits are important for the students appearing in the class 11th and 12th examinations. You may download the formula charts for Limits from the link below in a PDF Format.<\/p>\n<p><strong>You may also refer to the formula chart for the limits given below:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-731187\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/Screenshot-2024-08-29-160100.jpg\" alt=\"Limits Formula PDF \" width=\"257\" height=\"448\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/Screenshot-2024-08-29-160100.jpg 257w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/Screenshot-2024-08-29-160100-172x300.jpg 172w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/Screenshot-2024-08-29-160100-150x261.jpg 150w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/p>\n<p style=\"text-align: center;\">Must See &#8211; <strong><em><a href=\"https:\/\/infinitylearn.com\/surge\/maths\/average\/\"><span class=\"post post-post current-item\">Average<\/span><\/a><\/em><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limits_of_Trigonometric_Functions\"><\/span>Limits of Trigonometric Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Below is the list of the formulas for the trigonometric functions:<\/p>\n<ul>\n<li>lim<sub>x\u21920<\/sub> (sin x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (tan x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (cos x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (sin<sup>-1<\/sup> x) \/ x = 1<\/li>\n<li>lim<sub>x\u21920<\/sub> (tan<sup>-1<\/sup> x) \/ x = 1<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Limits_Properties\"><\/span>Limits Properties<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let us assume that lim<sub>x\u2192a<\/sub> f(x) and lim<sub>x\u2192a<\/sub> g(x) exist and let c be a constant. Therefore, below are the properties of the limits:<\/p>\n<ul>\n<li>lim<sub>x\u2192a<\/sub> (c \u00b7 f(x)) = c \u00b7 lim<sub>x\u2192a<\/sub> f(x)<br \/>\nA constant can be factored out from a limit.<\/li>\n<li>lim<sub>x\u2192a<\/sub> [f(x) + g(x)] = lim<sub>x\u2192a<\/sub> f(x) + lim<sub>x\u2192a<\/sub> g(x)<br \/>\nWe can add or subtract the limits as per the rule mentioned above.<\/li>\n<li>lim<sub>x\u2192a<\/sub> [f(x) \u00b7 g(x)] = lim<sub>x\u2192a<\/sub> f(x) \u00b7 lim<sub>x\u2192a<\/sub> g(x)<br \/>\nSimilar to the addition and subtraction property discussed above, we follow a similar rule for the multiplication of two or more limits.<\/li>\n<li>lim<sub>x\u2192a<\/sub> [f(x) \/ g(x)] = lim<sub>x\u2192a<\/sub> f(x) \/ lim<sub>x\u2192a<\/sub> g(x), provided that lim<sub>x\u2192a<\/sub> g(x) is not equal to zero.<br \/>\nSimilar to the addition and subtraction property discussed above, we follow a similar rule for the division of two limits.<\/li>\n<li>lim<sub>x\u2192a<\/sub> c = c<br \/>\nThe limit of a constant is always a constant.<\/li>\n<li>lim<sub>x\u2192a<\/sub> x<sup>n<\/sup> = a<sup>n<\/sup><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Limits_Practice_Questions\"><\/span>Limits Practice Questions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li>Check for the limit: limx0(sinx\u22c5x)<\/li>\n<li>Find the limit of the function: limx0(tanx\u22c5sinx)<\/li>\n<li>Evaluate the following limits:\n<ul>\n<li>limx0(sin2x)<\/li>\n<li>limx0(cos2x)<\/li>\n<li>limx0(tan2x)<\/li>\n<\/ul>\n<\/li>\n<li>Find the limit of the function: limx2(x2+6)<\/li>\n<li>Find the limit of the function: limx4(x4+25x)<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"Limits_Maths_Practice_FAQs\"><\/span>Limits Maths Practice FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_a_limit_in_calculus\"><\/span>What is a limit in calculus?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA limit describes how a function behaves as the input gets closer to a specific value. It helps us understand the function\u2019s value at that point, even if the function isn\u2019t defined there. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_find_the_limit_of_a_function_as_x_approaches_a_certain_value\"><\/span>How do you find the limit of a function as x approaches a certain value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo find the limit of a function f(x) as x approaches a value a, you look at how f(x) behaves as x gets closer to a. This can involve direct substitution, factoring, or other techniques to simplify the function. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_does_it_mean_if_the_limit_does_not_exist\"><\/span>What does it mean if the limit does not exist?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\t If the limit does not exist, it means that as x approaches the value, f(x) does not approach a single, finite number. This can occur if f(x) goes to infinity, oscillates wildly, or behaves unpredictably near the point. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is a limit in calculus?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A limit describes how a function behaves as the input gets closer to a specific value. It helps us understand the function\u2019s value at that point, even if the function isn\u2019t defined there.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you find the limit of a function as x approaches a certain value?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To find the limit of a function f(x) as x approaches a value a, you look at how f(x) behaves as x gets closer to a. This can involve direct substitution, factoring, or other techniques to simplify the function.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What does it mean if the limit does not exist?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"If the limit does not exist, it means that as x approaches the value, f(x) does not approach a single, finite number. This can occur if f(x) goes to infinity, oscillates wildly, or behaves unpredictably near the point.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>In Maths, a limit is defined as a value that a function approaches for the given input. Limits are an [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Limits in Maths","_yoast_wpseo_title":"Limits in Maths - Definition, Types, Functions, Properties and Questions","_yoast_wpseo_metadesc":"Learn about limits in maths, including their definition, types, functions, properties, and practice questions. Understand the foundational concepts of calculus with clear explanations and examples.","custom_permalink":"maths\/limits-in-maths\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Limits in Maths - Definition, Types, Functions, Properties and Questions<\/title>\n<meta name=\"description\" content=\"Learn about limits in maths, including their definition, types, functions, properties, and practice questions. 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