Results 1 to 2 of 2

Math Help - hard limit problem involving a trig. exponent

  1. #1
    Junior Member
    Joined
    Dec 2012
    From
    United States
    Posts
    35

    hard limit problem involving a trig. exponent

    PROBLEM:


    \lim_{x\to\(\pi^+)}{(1+3sinx)^{cot(x)}}


    ATTEMPT:

    Does L'Hopital's Rule apply work for this problem? I don't think so, because it is not in the appropriate indeterminate form; for, it would be 1^\infty. But I don't know any elementary methods that would be appropriate here, nor any limit properties. :/
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,160
    Thanks
    348

    Re: hard limit problem involving a trig. exponent

    Yes, L'Hospital's works. Try this - take the log of the expression, and you get:

    \lim ( \ln (1+3 \sinx)^{cotx}))= \lim ( \frac { \cos x \ln (1+3\sin x)}{\sin x})

    Now use L'Hospital's, and you shoud find that this limit approahes a value, let's call it A. The the limit of the original problem is  e^A.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 26th 2012, 12:59 AM
  2. kinda hard exponent problem
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 16th 2011, 12:41 PM
  3. Hard question involving trig and circles
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 7th 2010, 05:43 AM
  4. Replies: 3
    Last Post: May 5th 2009, 03:38 PM
  5. A difficult limit involving trig.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 31st 2006, 11:41 PM

Search Tags


/mathhelpforum @mathhelpforum