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

Ok, Limit problem

  • Thread starter aquitaine
  • Start date
  • #1
18
9
Ok, the problem is find the limit of x/sqrt(1-cosx) as x approaches 0 from the negative side.

First I tried simply applying l'hopital's rule to see what would happen, and it didn't work.

Next I tried rationalizing it by multiplying the numerator and denominator by sqrt(1+cosx), then using a trig identity (1-(cosx)^2=(sinx)^2 to get sqrt((sinx)^2) or simply sinx. Then I applied l'hopital's rule and ended up with a big mess that still ended up with 0/0.

Did I miss something or do something incorrectly?
 

Answers and Replies

  • #2
Vid
401
0
1 - cos(x) = 2sin^2(x/2)

x/sqrt(1-cos(x)) = x/sqrt(2)sin(x/2)

Using L'Hopitals on this does not lead to 0/0.
 
  • #3
18
9
So I was missing something, thanks.
 

Related Threads for: Ok, Limit problem

Replies
8
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
942
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
2K
Replies
0
Views
1K
Top