Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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:

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Show that if p is a positive integer, then $(\begin{array}{l} p \\ n \end{array}) = 0$ when $n > p$ , so $(1 + x)^{p} = \sum (\begin{array}{l} p \\ n \end{array}) x^{n}$ is just a sum of $p + 1$ terms, from $n = 0$ to $n = p$ . For example, $(1 + x)^{2}$ has $3$ terms, $(1 + x)^{3}$ has $4$ terms, etc. This is just the familiar binomial theorem.

Find the following limits using Maclaurin series and check your results by computer. Hint: First combine the fractions. Then find the first term of the denominator series and the first term of the numerator series.

$(a) \lim_{x \to 0} (\frac{1}{x} - \frac{1}{e^{x} - 1}) (b) \lim_{x \to 0} (\frac{1}{x^{2}} - \frac{\cos x}{\sin^{2} x}) (c) \lim_{x \to 0} (\csc^{2} x - \frac{1}{x^{2}}) (d) \lim_{x \to 0} (\frac{In (1 + x)}{x^{2}} - \frac{1}{x})$

Use power series to evaluate the function at the given point. Compare with computer results, using the computer to find the series, and also to do the problem without series. Resolve any disagreement in results (see Example 1). $\frac{1}{\sqrt{1 + x^{4}}} - c o s x^{2} a t x = 0.012$ at .

Solve for all possible values of the real numbers xand y in the following equations. $x + i y = {(1 - i)}^{2}$

Show that the binomial coefficients $(\begin{array}{l} - 1 \\ n \end{array}) = (- 1)^{n}$

See all solutions

Recommended explanations on Physics Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

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

Step by step solution

Maclaurin Series

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Magnetism

Fluids

Electromagnetism

Solid State Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

Company

Product

Help

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Magnetism

Fluids

Electromagnetism

Solid State Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

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