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Math Help - Using sine theta over theta equals 1 to find a limit

  1. #1
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    Using sine theta over theta equals 1 to find a limit

    <br /> <br />
\mathop {\lim }\limits_{x \to 2}  {{{xcsc2x} \over {cos5x}}}<br /> <br />

    I keep running into trouble with the x in front of cosecant... I don't know what to do with it, so I always end up with a x/1 which yields zero! (The answer in the book says the limit is 1/2).
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  2. #2
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    Quote Originally Posted by tom ato View Post
    <br /> <br />
\mathop {\lim }\limits_{x \to 2} {{{xcsc2x} \over {cos5x}}}<br /> <br />

    I keep running into trouble with the x in front of cosecant... I don't know what to do with it, so I always end up with a x/1 which yields zero! (The answer in the book says the limit is 1/2).
    Re-write as \lim_{x \to 2} \frac{x}{\sin 2x} \frac{1}{\cos 5 x }

    and use the fact that \lim _{x \to 0} \frac{ \sin kx}{x} = k
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