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Chapter 12: Q. (page 811)

Approximating f(x)=exIn calculus, it can be shown

that

f(x)=ex=鈭�xkk!k=o鈭�

We can approximate the value of f(x)=exfor any x using

the following sum:

f(x)=ex=鈭�xkk!k=on

for some n.

(a) Approximate f (1.3) with n = 4

(b) Approximate f (1.3) with n = 7.

(c) Use a calculator to approximate f (1.3).

(d) Using trial and error along with a graphing utility鈥檚

sequence mode, determine the value of n required to

approximate f (1.3) correct to eight decimal places.

Short Answer

Expert verified

a.

b.

c.

d.

Step by step solution

01

step 1.Given information

Given f(x)=ex=鈭�xkk!k=on

here x=1.3and n=4

e1.3=鈭�1.3kk!k=04

=(1.30+1.31+1.322!+1.333!+1.34!4)

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Most popular questions from this chapter

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

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In Problems 17鈥�28, write down the first five terms of each sequence.

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In Problems 61鈥�70, express each sum using summation notation.

a+ar+ar2+.....+arn-1

In Problems 71-82, find the sum of each sequence.

鈭�k3k=520

In Problems 61鈥�70, express each sum using summation notation.

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