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

Limit of a function

  • Thread starter francisg3
  • Start date
  • #1
32
0
find the limit of lim ⁡(x*cos x-sin x)/(x-sin⁡x)
(x→0)



I know substitution does not work as it gives 0/0 and I attempted to factor and try the conjugate method without any result. I also tried L'Hopitals rule which states that i take the derivative of the numerator and denominator which gave the following results:

lim x-> 0 = (cos x -xsin x-cos x)/(1-cos x) which still gives me 0/0
 
Last edited:

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
13
Use L'Hopital's again, but first simplify the numerator.
 
  • #3
You have to apply l'hopitals repeatedely for this guy or use the power series of sinx and cosx.
 
  • #4
32
0
alright so i applied l'hopitals again to
(-x*sin x)/(1-cos x) simplified version of the first derivative...then i dervied again to get

(-sin x - x*cos x)/(sin x) which itook the derivative once again to give:

(-cos x - cos x + x*sin x)/(cos x) which gives me a limit of -2...i have gone wrong somewhere
 
  • #5
Char. Limit
Gold Member
1,204
13
alright so i applied l'hopitals again to
(-x*sin x)/(1-cos x) simplified version of the first derivative...then i dervied again to get

(-sin x - x*cos x)/(sin x) which itook the derivative once again to give:

(-cos x - cos x + x*sin x)/(cos x) which gives me a limit of -2...i have gone wrong somewhere
Don't know why you think that... -2 is the answer I get.
 
  • #6
631
0
alright so i applied l'hopitals again to
(-x*sin x)/(1-cos x) simplified version of the first derivative...then i dervied again to get

(-sin x - x*cos x)/(sin x) which itook the derivative once again to give:
Don't take the derivative again, this has a definite limit.
 
  • #7
Char. Limit
Gold Member
1,204
13
Don't take the derivative again, this has a definite limit.
...no it doesn't...
 
  • #8
32
0
You are right Char. Limit, my mistake. Thanks for your help!
 
  • #9
631
0
...no it doesn't...
Eek I took x/Sin x = 1 in my head *headdesk*
 
Last edited:
  • #10
Char. Limit
Gold Member
1,204
13
Eek I took x/Sin x = 1 in my head *headdesk*
No problem. Just making sure the OP gets it right is all.
 

Related Threads for: Limit of a function

  • Last Post
Replies
4
Views
583
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
868
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
1K
Top