Maclaurin

Maclaurin series for common functions, constructing and manipulating series using differentiation, integration, addition, multiplication, division and composition, and using series to approximate functions, expand rational powers and evaluate limits.

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Maclaurin Series Basics

Maclaurin

Maclaurin series express a function as a polynomial in powers of \(x\) using derivatives at \(0\), with general form \(f\left(x\right)=\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^{n}}{n!}\), and include standard expansions for \(e^x\), \(\sin x\), \(\cos x\), \(\ln\left(x+1\right)\), \(\arctan x\), and the binomial extension for rational exponents.

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Operations on Maclaurin Series

Maclaurin

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Maclaurin

Maclaurin series for common functions, constructing and manipulating series using differentiation, integration, addition, multiplication, division and composition, and using series to approximate functions, expand rational powers and evaluate limits.