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Math Help - limit help

  1. #1
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    limit help

    lim (1+tanx)^(1/2) - (1+sinx)^(1/2)
    x->0 _____________________________
    x3



    how do you do this? the conjugate is no help!
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  2. #2
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    Re: limit help

    Is this \displaystyle \begin{align*} \lim_{x \to 0}\frac{\left( 1 + \tan{x} \right)^{\frac{1}{2}} - \left( 1 + \sin{x} \right)^{\frac{1}{2}}}{x^3} \end{align*}?
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  3. #3
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    Re: limit help

    yes so how do i go about applying the limit?
    Quote Originally Posted by Prove It View Post
    Is this \displaystyle \begin{align*} \lim_{x \to 0}\frac{\left( 1 + \tan{x} \right)^{\frac{1}{2}} - \left( 1 + \sin{x} \right)^{\frac{1}{2}}}{x^3} \end{align*}?
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  4. #4
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    Re: limit help

    Unfortunately, you have apparently already decided that "the conjugate is no help" and that is certainly the method I would suggest! It also helps to know the basic limit, \lim_{x\to 0} sin(x)/x= 1.

    Or, just calculating that quantity for, say x= 0.00001 should give you a good idea.
    Last edited by HallsofIvy; October 11th 2012 at 12:00 PM.
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  5. #5
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    Re: limit help

    well i know the answer should be 1/4 but i still dont know how to get that or what to do?
    Quote Originally Posted by HallsofIvy View Post
    Unfortunately, you have apparently already decided that "the conjugate is no help" and that is certainly the method I would suggest! It also helps to know the basic limit, \lim_{x\to 0} sin(x)/x= 1.

    Or, just calculating that quantity for, say x= 0.00001 should give you a good idea.
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