# Solutions to Problem Set 29

Math 211-03

11-16-2017

[Remainder Term]

1. Write down the remainder term for .

2. Write down the remainder term for .

I can see that . So

3. Write down the remainder term for .

I can see that . So

4. Use the remainder term to estimate the largest possible error in using the degree Taylor polynomial to approximate for .

Since , I have . Moreover, , so

Thus,

5. Using the remainder term, find the minimum number n so that the degree Taylor polynomial for will approximate on the interval to an error of less than .

I can see that . So

Since , I have . Also , so . So

(I used the fact that .)

I want to find the smallest n for which this is less than .

The first n for which is less than is .

You probably wouldn't worry about what people think of you if you could know how seldom they do. - Olin Miller

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