Using your phone's internet browser
go to:  qna.rediff.com
Click and drag this link to
the Home icon in your browser.
Q.

Lim (x-->pi) ((1-sin(x/2)) /(cos(x/2) * (cos (x/4) -sin (x/4)))?
Don't use L'hopitals Rule

Tags: don, sin, lim
Asked by sanjeev, 18 Feb '12 12:20 pm
  Invite a friend  |  
  Save  |  
 Earn 10 points for answering
Answer this question  Earn 10 points for answering    
4000 characters remaining  
  
    
Keep me signed inNew User? Sign up

Answers (1)

 
1.

Lim (x) ((1-sin(x/2)) /(cos(x/2) * (cos (x/4) -sin (x/4)))
= lim (x) [(1-sin(x/2)*(1 + sin(x/2)] /[(cos(x/2) * (1 + sin(x/2) * (cos (x/4) -sin (x/4))]
= lim (x) [(1-sin^2 (x/2)] /[(cos(x/2) * (1 + sin(x/2) * (cos (x/4) -sin (x/4))]
= lim (x) [(cos^2 (x/2)] /[(cos(x/2) * (1 + sin(x/2) * (cos (x/4) -sin (x/4))]
= lim (x) [(cos (x/2)] /[(1 + sin(x/2) * (cos (x/4) -sin (x/4))]
= lim (x) [(cos^2 (x/4) - sin^2 (x/4)] /[(1 + sin(x/2) * (cos (x/4) -sin (x/4))]
= lim (x) [(cos (x/4) + sin (x/4)] /[(1 + sin(x/2)]
= (1/2 + 1/2) / (1 + 1)
= 1/2.
Answered by anju chauhan, 18 Feb '12 12:24 pm

 
  
Report abuse
Useful
 (0)
Not Useful
 (0)
Your vote on this answer has already been received

Ask a Question

Get answers from the community

600 characters remaining