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Chapter 1: Q25P (page 1)

Question: Find the first few terms of the Maclaurin series for each of the following functions and check your results by computer. $\frac{2 X}{e^{2 x} - 1}$

Short Answer

Expert verified

Hence, the required series is: .

Step by step solution

Maclaurin Series

Maclaurin series is basically a type of power series expansion of the function f(x) about the origin, with all the terms having positive values expanded as:

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Most popular questions from this chapter

The following series are not power series, but you can transform each one into a power series by a change of variable and so find out where it converges. 

$\sum_{n = 0}^{\infty} \frac{(- 1)^{n} (x)^{\frac{1}{2}}}{nlnn}$

Find the interval of convergence of each of the following power series; be sure to investigate the endpoints of the interval in each case $\sum_{n = 1}^{\infty} \frac{(- 1)^{n} x^{n}}{n (n + 1)}$ .

$In \cos x$ Hints:Method1:Write $\cos x = 1 + (\cos x - 1) = 1 + u$ ;use the series you know for $In (1 + u)$ ;replace u by the Maclaurin series for $(\cos x - 1)$

Method2: $In \cos x =$ $- \int_{0}^{x} \tan udu$ Use the series of Example 2 in method B.

$\frac{1 + x}{1 - x}$

$f (x) = s i n x, a = π / 2$

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Question: Find the first few terms of the Maclaurin series for each of the following functions and check your results by computer. 2Xe2x-1

Short Answer

Step by step solution

Maclaurin Series

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Question: Find the first few terms of the Maclaurin series for each of the following functions and check your results by computer. $\frac{2 X}{e^{2 x} - 1}$