Bound for Taylor Series Error

  • Thread starter francisg3
  • Start date
  • #1
32
0
Had a recent homework questions:
Find a bound for the error |f(x)-P3(x)| in using P3(x) to approximated f(x) on the interval [-1/2,1/2]
where f(x)=ln(1+x) abd P3(x) refers to the third-order Taylor polynomial.

I found the Taylor series of f(x) seen below:

x- x^2/2!+(2x^3)/3!

I know the Taylor series expression has a remainder which in this case would be the 4th order polynomial and beyond but I am completely lost beyond this. Any help would be greatly appreciated!
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,557
767
Your formula for the remainder after n = 3 is

[tex]\frac{f^{(4)}(c)}{4!}(x-a)^4[/tex]

Your a = 0. How large in absolute value can this be for x and c in your given interval?
 

Related Threads on Bound for Taylor Series Error

Replies
7
Views
3K
Replies
1
Views
662
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
6
Views
2K
Replies
0
Views
9K
Replies
3
Views
4K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
1
Views
637
Replies
0
Views
1K
Top