Results 1 to 3 of 3

Math Help - L' Hospital's Rule

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    43

    L' Hospital's Rule

    find the limits of the following:

    1)arctan(x)/[(1/x)-7]
    lim=infinity

    for this I got [(1)/(1+x^2)]/(-1/x^2) but it still is 0.

    2) [1-cos(8x)]/[1-cos(9x)]
    lim=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    For the first one you don't need L'Hopital, notice that \lim_{x \rightarrow \infty } \arctan(x)= \pi /2 and \lim_{ x\rightarrow \infty } \frac{1}{x} -7 = -7 so the limit should be -\pi /14 (you should also make sure the hypothesis for L'Hopital's rule apply in each case, in this case they don't)

    For the second one use L'Hopital twice
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Asuhuman18 View Post
    find the limits of the following:

    1)arctan(x)/[(1/x)-7] Mr F says: This is not an indeterminant form so
    lim=infinity ..............................it's not valid to apply l'Hopital's Rule.

    for this I got [(1)/(1+x^2)]/(-1/x^2) but it still is 0.

    2) [1-cos(8x)]/[1-cos(9x)]
    lim=0
    Where are you stuck with 2)? Apply l'Hopital's rule twice and then take the limit. If you need more help, please show what you've done and say where you get stuck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. without using L'Hospital's Rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 31st 2010, 02:48 AM
  2. L'Hospital's rule
    Posted in the Calculus Forum
    Replies: 8
    Last Post: February 16th 2010, 08:37 PM
  3. L'Hospital's Rule
    Posted in the Calculus Forum
    Replies: 10
    Last Post: December 9th 2009, 04:26 PM
  4. L'Hospital's rule
    Posted in the Calculus Forum
    Replies: 10
    Last Post: November 19th 2009, 08:31 PM
  5. L'Hospital's Rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 15th 2008, 08:24 PM

Search Tags


/mathhelpforum @mathhelpforum