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Chapter 1: Q9P (page 32)

1+x1-x

Short Answer

Expert verified

The series is 1+x1-x=1+鈭�n=1鈭�2xn.

The sum is given below.

S1=1+2x

S2=1+2x+2x2

S3=1+2x+2x2+2x3

The graphs are shown below.

Step by step solution

01

 Step 1: Given Information

The Maclaurin series.

02

Definition of the MaclaurinSeries.

A Maclaurin series is a function with an expansion series that gives the sum of the function's derivatives.

03

Find the series and sum.

The Maclaurin series is given below.

1+x1-x=1+2x+2x2+2x3+鈥�

The general series is given below.

1+x1-x=1+鈭�n=1鈭�2xn

The sum is given below.

S1=1+2x

S2=1+2x+2x2

S3=1+2x+2x2+2x3

04

Plot the graphs.

The graph of the function with S1,S2,S3is given below.

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Most popular questions from this chapter

Test the following series for convergence.

4.鈭�n=1鈭�(鈭�3)nn!

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).In(x+1+x2)-sinxatx=0.001.

f(x)=cotx,a=蟺2

Show thatis the distance between the points and in the complex plane. Use this result to identify the graphs in Problems 53,54,59,and60without computation.

The velocityof electrons from a high energy accelerator is very near the velocityof light. Given the voltage Vof the accelerator, we often want to calculate the ratio v / c. The relativistic formula for this calculation is (approximately, forV鈮�1)

vc=1-(0.511V)2, V=Number of million volts

Use two terms of the binomial series (13.5) to find1 - v/cin terms ofV. Use your result to find 1 - v/cfor the following values of V. Caution: V= the number of millionvolts.

(a) V =100 million volts

(b)V =500 million volts

(c)V =25,000 million volts

(d)V =100 gigavolts (100109 volts105 million volts)
See all solutions

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