<p>Given any well-behaved function $\mathrm{f}(x)$, using Maclaurin’s series expansion, it can be expressed as a Polynomial of $x$:</p>
<p style="text-align: center">$\mathrm{f}(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{3}}{{x}^{3}}+....+{{a}_{n}}{{x}^{n}}$</p>
<p>The series’ accuracy increases when:</p>
<ol class="num-list"><li><div class="list-item-paragraph">more terms are used.</div></li><li><div class="list-item-paragraph">when the value of $x$ is close to zero.</div></li></ol>

Given any well-behaved function $\mathrm{f}(x)$, using Maclaurin’s series expansion, it can be expressed as a Polynomial of $x$:

$\mathrm{f}(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{3}}{{x}^{3}}+....+{{a}_{n}}{{x}^{n}}$

Maclaurin Series and Power Series - General

Maclaurin Series and Power Series

International Baccalaureate Higher Level Mathematics

Maclaurin Series and Power Series - Maclaurin Series and Power Series - General

Maclaurin Series and Power Series - Maclaurin Series and Power Series - General