Results 1 to 5 of 5

Math Help - indeterminate form

  1. #1
    Member
    Joined
    Dec 2007
    Posts
    137

    Question indeterminate form

    I'm having trouble figuring this one out:

    \lim_{x\to0^+}sin(x)ln(x)

     = \lim_{x\to0^+}\frac{sin(x)}{\frac{1}{ln(x)}}

     = \lim_{x\to0^+}\frac{cos(x)}{\frac{-1}{x(ln(x))^2}}

    Which doesn't seem to help very much.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by xxlvh View Post
    I'm having trouble figuring this one out:

    \lim_{x\to0^+}sin(x)ln(x)

     = \lim_{x\to0^+}\frac{sin(x)}{\frac{1}{ln(x)}}

     = \lim_{x\to0^+}\frac{cos(x)}{\frac{-1}{x(ln(x))^2}}

    Which doesn't seem to help very much.

    Do it the other way: \frac{\ln x}{\frac{1}{\sin x}} and then "separate" the result in two convenient factors.

    The limit is zero.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2007
    Posts
    137
    Sorry, I'm still puzzled on how to "separate" them?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    \sin (x)\ln (x)=\frac{\sin x}{x}\cdot x\ln x.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Krizalid View Post
    \sin (x)\ln (x)=\frac{\sin x}{x}\cdot x\ln x.

    This, of course, is much better and simpler than what I proposed, which was:

    \lim_{x\to 0}\sin x\ln x =\lim_{x\to 0} \frac{\ln x}{\frac{1}{\sin x}}=\lim_{x\to 0}\frac{\frac{1}{x}}{\frac{-\cos x}{\sin^2x}}=\lim_{x\to 0}-\frac{\sin x}{x}\frac{\sin x}{\cos x} =(-1)\cdot 0=0

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Of an indeterminate form 0/0
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 7th 2010, 11:02 PM
  2. Limit of an Indeterminate Form
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 23rd 2010, 05:41 PM
  3. Indeterminate Form
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 29th 2009, 06:31 AM
  4. Limit with Indeterminate Form
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 22nd 2009, 01:27 PM
  5. limits indeterminate form
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 8th 2007, 07:13 PM

Search Tags


/mathhelpforum @mathhelpforum