{"id":155494,"date":"2022-03-26T00:42:29","date_gmt":"2022-03-25T19:12:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/differential-calculus-and-approximations-explanation-and-solved-example\/"},"modified":"2023-01-02T12:51:34","modified_gmt":"2023-01-02T07:21:34","slug":"differential-calculus-and-approximations-explanation-and-solved-example","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/differential-calculus-and-approximations\/","title":{"rendered":"Differential Calculus and Approximations \u2013 Explanation and Solved Example"},"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\/differential-calculus-and-approximations\/#Approximation_of_Differential_Equation\" title=\"Approximation of Differential Equation\">Approximation of Differential Equation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/differential-calculus-and-approximations\/#Approximation_Example\" title=\"Approximation Example\">Approximation Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/differential-calculus-and-approximations\/#Riemann_Sum_Example\" title=\"Riemann Sum Example\">Riemann Sum Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/differential-calculus-and-approximations\/#Problems_for_Practice\" title=\"Problems for Practice\">Problems for Practice<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Approximation_of_Differential_Equation\"><\/span>Approximation of Differential Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Differential equations are mathematical equations that describe the change in a certain quantity, or function, over time. In order to approximate a differential equation, a numerical method is used to approximate the solution to the equation. This involves breaking the differential equation down into a series of smaller, simpler equations, which can then be solved using a computer. The approximation of a differential equation is used to calculate the approximate solution to the equation, which can be used to predict the behavior of the quantity or function over time.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155493 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/differential-calculus-and-approximations-explanation-and-solved-example.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/differential-calculus-and-approximations-explanation-and-solved-example.jpg?v=1648235547 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/differential-calculus-and-approximations-explanation-and-solved-example-300x212.jpg?v=1648235547 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Approximation_Example\"><\/span>Approximation Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In the approximation example, we will approximate the value of pi. Pi is the ratio of a circle&#8217;s circumference to its diameter and is approximately 3.14.<\/p>\n<p>We will use the following equation to approximate pi:<\/p>\n<p>pi \u2248 (C\/d)^2<\/p>\n<p>In this equation, C is the circumference of the circle and d is the diameter of the circle.<\/p>\n<p>We can use the value of C and d from a circle with a diameter of 10 cm and a circumference of 31.4 cm.<\/p>\n<p>pi \u2248 (31.4 cm\/10 cm)^2<\/p>\n<p>pi \u2248 3.14<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Riemann_Sum_Example\"><\/span>Riemann Sum Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A Riemann sum is a way to estimate the value of a function over an interval by adding up the function values at evenly spaced points within the interval.<\/p>\n<p>The example below illustrates how to find a Riemann sum for a function over the interval [0, 3].<\/p>\n<p>The function being estimated is f(x) = x^3.<\/p>\n<p>The points at which the function is evaluated are:<\/p>\n<p>0, 1, 2, and 3.<\/p>\n<p>The width of the interval is 1.<\/p>\n<p>The sum of the function values at the points evaluated is:<\/p>\n<p>0 + 1 + 4 + 9 = 14.<\/p>\n<p>Thus, the Riemann sum for the function over the interval [0, 3] is 14.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problems_for_Practice\"><\/span>Problems for Practice<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Problem 1<\/p>\n<p>A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service.<\/p>\n<p>C = 25 + 50h<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Approximation of Differential Equation Differential equations are mathematical equations that describe the change in a certain quantity, or function, over [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Differential Calculus and Approximations","_yoast_wpseo_title":"Differential Calculus and Approximations \u2013 Explanation and Examples?","_yoast_wpseo_metadesc":"Learn about Differential Calculus and Approximations topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/differential-calculus-and-approximations\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin 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