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Math Help - Find the limits of the following in all steps:

  1. #1
    Newbie Alexaax3's Avatar
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    Jun 2009
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    Smile Find the limits of the following in all steps:

    Hey i am not really good with limits that have sin,cos, and etc so i was wondering if i could have some help with these 2 questions in finding the limits.

    A) lim[sin(1-√x )] / (x-1)
    x>>1

    B) lim cos(π/ √19-3 sec 2t )
    t>>0
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  2. #2
    Senior Member Twig's Avatar
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    Mar 2008
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    Gothenburg
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    Hi

    Im not sure what you mean on the second one.

    First one:

     \displaystyle\lim_{x\to1} \frac{sin(1-\sqrt{x})}{x-1}=\displaystyle\lim_{x\to1}-\frac{sin(1-\sqrt{x})}{(1-\sqrt{x})(1+\sqrt{x})} =-\frac{1}{2}

    I used the fact that  (1-x)=(1-\sqrt{x})(1+\sqrt{x}) on the denominator to be able to use the standard limit.
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  3. #3
    Newbie Alexaax3's Avatar
    Joined
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    Quote Originally Posted by Twig View Post
    Hi

    Im not sure what you mean on the second one.

    First one:

     \displaystyle\lim_{x\to1} \frac{sin(1-\sqrt{x})}{x-1}=\displaystyle\lim_{x\to1}-\frac{sin(1-\sqrt{x})}{(1-\sqrt{x})(1+\sqrt{x})} =-\frac{1}{2}

    I used the fact that  (1-x)=(1-\sqrt{x})(1+\sqrt{x}) on the denominator to be able to use the standard limit.
    \

    Oh thankyou so much, thats the same answer i got for the first one but i thought i did it wrong cuz i did it with cosine, but thanks still that helped alot
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