Results 1 to 10 of 10

Math Help - Finding the limit

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    12

    Finding the limit

    okay

    so I am trying to find the limit. LIM sin (squared) 3x / x (squared) x--> 0

    I am soo unsure of how to do this. Any suggestions?? btw we havent gone over the L'H rule yet...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by MZTakara View Post
    okay

    so I am trying to find the limit. LIM sin (squared) 3x / x (squared) x--> 0

    I am soo unsure of how to do this. Any suggestions?? btw we havent gone over the L'H rule yet...
    \displaystyle\lim_{x\to 0}\frac{\sin^2(3x)}{x^2}=\lim_{x\to 0}\frac{9(\sin^2(3x))}{(3x)^2}=9\cdot\lim_{x\to 0}\left(\frac{(\sin(3x))}{(3x)}\right)^2=\cdots
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    For small values of x,  \sin x \approx x .
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Use this guy

    \displaystyle \lim_{x\to 0} \frac{\sin x }{x} = 1

    Make

    \displaystyle  \frac{\sin^2 3x }{x} = \frac{\sin 3x }{x}\times \frac{3}{3}\times  \frac{\sin 3x }{1}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2011
    Posts
    12
    but sin is squared....that does not matter???
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by dwsmith View Post
    \displaystyle\lim_{x\to 0}\frac{\sin^2(3x)}{x^2}=\lim_{x\to 0}\frac{9(\sin^2(3x))}{(3x)^2}=9\cdot\lim_{x\to 0}\left(\frac{(\sin(3x))}{(3x)}\right)^2=\cdots
    \displaystyle9\cdot\lim_{x\to 0}\left(\frac{(\sin(3x))}{(3x)}\right)^2=\cdots

    Let 3x = t

    \displaystyle\lim_{t\to 0}\left(\frac{(\sin(t))}{(t)}\right)^2=\cdots

    What is 1 squared?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2011
    Posts
    12
    one....>_>

    Thanks
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Quote Originally Posted by MZTakara View Post
    but sin is squared....that does not matter???
    No.  \sin^{2}(3x) = \sin(3x)* \sin(3x) \approx 3x*3x = 9x^{2} for small values of x.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Jan 2011
    Posts
    12
    lol..ima so fail this semester.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,547
    Thanks
    1418
    Quote Originally Posted by MZTakara View Post
    lol..ima so fail this semester.
    Not when you've got MHF to turn to when you're feeling low :P
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding limit of this function, using Limit rules
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 27th 2011, 01:12 PM
  2. Finding a limit. Finding Maclaurin series.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 18th 2010, 10:04 PM
  3. finding a limit
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 4th 2009, 06:46 AM
  4. Finding this limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 3rd 2008, 01:09 PM
  5. help finding the following limit:
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 15th 2008, 09:25 PM

Search Tags


/mathhelpforum @mathhelpforum