   Chapter 11.11, Problem 10E

Chapter
Section
Textbook Problem

# Find the Taylor polynomial T3(x) for the function f centered at the number a. Graph f and T3 on the same screen.10. f(x) = tan−1 x, a = 1

To determine

To find: The Taylor polynomial T3(x) for f(x)=tan1x centered at a=1 and then graph f and the polynomial.

Explanation

Formula used:

Taylor polynomial:

Let nth degree Taylor polynomial of f at a is denoted by Tn(x) and is defined as,

Tn(x)=i=0nf(i)(a)i!(xa)i=f(a)+f(a)1!(xa)+f(a)2!(xa)2++f(n)(a)n!(xa)n

And f is the sum of its Taylor series, f(x)=n=0f(n)(a)n!(xa)n.

Calculation:

The given function is f(x)=tan1x, centered at a=1.

The first derivative of f(x) is f(x)=1x2+1 and the corresponding value at a=1 is f(1)=12.

The second derivative is f(x)=2x(x2+1)2 and the corresponding value at a=1 is f(1)=12.

The third derivative is f(x)=2(3x2+1)(x2+1)3 and the corresponding value at a=1 is f(1)=12

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 