Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By KevinShaughnessy
  • 1 Post By Prove It

Math Help - Problem trying to find limit of trigonometric function

  1. #1
    Junior Member
    Joined
    Jan 2013
    From
    Montreal
    Posts
    65
    Thanks
    1

    Problem trying to find limit of trigonometric function

    Hi,

    I'm given the problem of finding the limit as x approaches 0 of tan3x/tan5x. To start, I replace tan with sin/cos, so that I get sin3x/cos3x/sin5x/cos5x. My professor wrote it out as sin3x/1 1/sin5x cos5x1/cos3x. He then somehow found a way to get a 3x to the denominator of the first term after factoring out a 3/5, and add 5x to the numerator of the second term. I'm not sure how he managed that, could someone help me to understand?

    Thanks!

    Kevin
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jan 2013
    From
    Montreal
    Posts
    65
    Thanks
    1

    Re: Problem trying to find limit of trigonometric function

    I think I got it: he added 5x to the denominator of the first term and to the numerator of the second term, which both cancel out so is the same as multiplying by 1. He then multiplied the first term by 3/3, factored out 3/5, and was left with an easily solvable limit?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293

    Re: Problem trying to find limit of trigonometric function

    Quote Originally Posted by KevinShaughnessy View Post
    Hi,

    I'm given the problem of finding the limit as x approaches 0 of tan3x/tan5x. To start, I replace tan with sin/cos, so that I get sin3x/cos3x/sin5x/cos5x. My professor wrote it out as sin3x/1 1/sin5x cos5x1/cos3x. He then somehow found a way to get a 3x to the denominator of the first term after factoring out a 3/5, and add 5x to the numerator of the second term. I'm not sure how he managed that, could someone help me to understand?

    Thanks!

    Kevin
    First, you need to know that \displaystyle \begin{align*} \lim_{x \to 0}\frac{\tan{(x)}}{x} = 1 \end{align*}. This should be obvious if you already know the standard limit \displaystyle \begin{align*} \lim_{x \to 0}\frac{\sin{(x)}}{x} = 1 \end{align*}. Then

    \displaystyle \begin{align*} \lim_{x \to 0} \frac{\tan{(3x)}}{\tan{(5x)}} &= \lim_{x \to 0} \left[ \frac{15x}{15x} \cdot \frac{\tan{(3x)}}{\tan{(5x)}} \right] \\ &= \frac{3}{5} \lim_{x \to 0} \left[ \frac{\tan{(3x)}}{3x} \cdot \frac{5x}{\tan{(5x)}} \right] \end{align*}

    I'm sure you can go from here.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit of a trigonometric function
    Posted in the Calculus Forum
    Replies: 9
    Last Post: March 19th 2013, 02:21 PM
  2. Replies: 5
    Last Post: January 28th 2013, 06:44 PM
  3. Find the (trigonometric) limit
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 14th 2009, 07:52 PM
  4. Limit of a Trigonometric Function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 15th 2009, 06:56 PM
  5. Limit of trigonometric function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 13th 2008, 12:55 PM

Search Tags


/mathhelpforum @mathhelpforum