Results 1 to 2 of 2

Math Help - L'Hopital's Rule

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    178

    L'Hopital's Rule

    f(x)= \frac{1- cos (x)}{x + x^2}

    Find the error in the following incorrect application of L'Hopital's rule.

    \frac{f'(x)}{g'(x)}= \frac{sin (x)}{1 + 2x}
    \frac{f''(x)}{g''(x)}= \frac{cos (x)}{2}

    Therefore, the lim x--> 0 = \frac{1}{2}.


    I'm not sure what the problem is. My guess is that it has something to do with ignoring the 0 (that came from the derivative of 1) on the numerator of the 2nd derivative.

    I know the value of 0 plugged in is correct. There didn't appear any faulty differentiation.

    Another thought is that I should use a trig rule.
    1 - cos (x) looks like it should be replaced by something.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    \frac{1-\cos x}{x+x^2}\to\frac00 as x\to0, and \frac{\sin x}{1+2x}\to0 as x\to0, hence, there's no reason to differentiate again since there's no indeterminate form.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. L' Hopital's Rule
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 26th 2010, 11:08 AM
  2. L'Hopital's Rule
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 28th 2009, 05:40 PM
  3. líHopitalís Rule Help..
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 27th 2009, 11:06 PM
  4. L'hopital Rule qn
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 26th 2008, 10:36 AM
  5. L'Hopital Rule
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 8th 2008, 04:00 PM

Search Tags


/mathhelpforum @mathhelpforum