• Support PF! Buy your school textbooks, materials and every day products Here!

Calculate limit using taylor series

  • Thread starter Hernaner28
  • Start date
  • #1
263
0

Homework Statement



Calculate: $$ \displaystyle \underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos \left( 1-\cos x \right)}{{{x}^{4}}}$$

Homework Equations





The Attempt at a Solution



Using Taylor series I have:

$$ \displaystyle f'\left( x \right)=\sin \left( 1-\cos x \right)\sin x$$

$$\displaystyle f'\left( 0 \right)=0$$

but as you can see, now it turns very tedious to continue differentiating. Do I have to keep differentiating until I get something? Or is there any quicker way to compute this?

Thanks
 

Answers and Replies

  • #2
938
9
There is. All you need to use is the Taylor series for cos(x). Also remember that since you're taking limit of x->0, you only need to carry with you the terms of the lowest non-trivial order.
 

Related Threads on Calculate limit using taylor series

  • Last Post
Replies
11
Views
1K
Replies
0
Views
3K
Replies
2
Views
627
Replies
27
Views
2K
  • Last Post
Replies
1
Views
810
  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
17
Views
3K
Replies
6
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
6
Views
1K
Top