Taylor series centered at a ? 0a. Find the first four

Chapter 8, Problem 20E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Taylor series centered at \(a \neq 0\)

a. Find the first four nonzero terms of the Taylor series for the given function centered at a.

b. Write the power series using summation notation.

f(x) = 1/x, a = 2

Questions & Answers

QUESTION:

Taylor series centered at \(a \neq 0\)

a. Find the first four nonzero terms of the Taylor series for the given function centered at a.

b. Write the power series using summation notation.

f(x) = 1/x, a = 2

ANSWER:

Solution 20E

Step 1:

  1.  In this problem we need to find  first four nonzero terms of the taylor series for the function f(x) =   , centered at  a = 2 .

We know that , the taylor series of the function centered  at ‘a’ is :

 f(x) = f(a) + (x-a)++

Given  ; f(x) = , centered at a = 2.

          f(x)  =  , then  f(2) =

          , then   , since

           = , then  

         

          = , then   ………………

Therefore , the taylor series of the function  f(x) = , centered at a = 2is ;

 f(x) =  = f(2) +(x-2)++

           = + (x-2)++

           = - (x-2)+-

Therefore , the first four nonzero terms of the taylor series centered at ‘2’ for the function  ’ are - (x-2)+-

That is ,  ,-(x-2) ,,-

First term =

Second term = -(x-2)

Third term =

Fourth term =

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back