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Chapter 8: Q. 52 (page 692)

Find the Maclaurin series for the functions in Exercises 51鈥�60 by substituting into a known Maclaurin.

Also, give the interval of convergence for the series.

e-3x2

Short Answer

Expert verified

The required Maclaurin series is e-3x2=鈭�k=0鈭�(-3)kx2kk!

Step by step solution

01

Step 1. Given Information

Consider the functionf(x)=e-3x2

02

Step 2

We know that the Maclaurin series for the function g(x)=exis ex=鈭�k=0鈭�xkk!

So, to find the Maclaurin series of the function f(x)=e-3x2, we replace xby -3x2in the Maclaurin series of the function ex

Therefore, e-3x2=鈭�k=0鈭�-3x2kk!implies that e-3x2=鈭�k=0鈭�(-3)kx2kk!

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Most popular questions from this chapter

Explain why 鈭�k=0鈭�x-kk is not a power series.

Let ak鈮�0for each value of k, and let 鈭�k=0鈭�鈥�akxkbe a power series in xwith a positive and finite radius of convergence p. What is the radius of convergence of the power series鈭�k=0鈭�鈥�1akxk?

Find the interval of convergence for power series:鈭�k=0鈭�-1k2k+1!3x+72k+1

Find the interval of convergence for power series: 鈭�k=1鈭�1k(x+2)k

Use an appropriate Maclaurin series to find the values of the series in Exercises 17鈥�22.
鈭�k=0鈭�-蟺kk!
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