Results 1 to 3 of 3

Math Help - Evaluate The Following Limit. (1)

  1. #1
    Member
    Joined
    Jan 2009
    Posts
    236

    Evaluate The Following Limit. (1)

    Hi

    Evaluate the following limit :
    \lim_{x\to0} \frac{sinh(x) - sin(x)}{sin^3(x)}
    I used L`Hospital`s, But I stucked.
    I tried to use the sandwich theorem:

    Clearly |\frac{sinh(x) - sin(x)}{sin^3(x)}| \leq -(sinh(x)-sin(x))
    Since the minumum value for sin^3(x) is -1.
    since I make the denominator smaller then the whole fraction is bigger.
    and since -\lim_{x\to0} (sinh(x)-sin(x)) = 0
    then ,By using the sandwich theorem, the desired limit =0
    Is this right?

    Do you have another way to make the limit simpler ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    L'hopital's rule will work if you apply it 3 times--there might be a better way

    you should get 1/3
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    Posts
    236
    Quote Originally Posted by Calculus26 View Post
    L'hopital's rule will work if you apply it 3 times--there might be a better way

    you should get 1/3
    Thanks.
    This means my solution(using sandwich theorem) is wrong.

    Still searching for professional solutions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Evaluate the following limit
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 6th 2010, 09:36 AM
  2. Evaluate The Following Limit. (3)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 16th 2010, 06:53 AM
  3. How do you evaluate a limit
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 2nd 2009, 09:37 AM
  4. evaluate the limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 19th 2009, 06:01 PM
  5. To Evaluate the following limit...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2009, 12:06 PM

Search Tags


/mathhelpforum @mathhelpforum