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Math Help - Trig Limit

  1. #1
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    Trig Limit

    Hey

    I know this question is rather simple but I just can't seem to get it...

    \displaystyle\lim_{x\rightarrow0}\frac{sin 5x}{sin 2x}-\frac{sin 3x}{4x}

    Thanks
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  2. #2
    TD!
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    You know the standard limit of sin(a)/a for a->0? It's 1. Rewrite:

    <br />
\lim_{x\rightarrow0}\left( \frac{\sin 5x}{\sin 2x}-\frac{\sin 3x}{4x} \right) =<br />
\lim_{x\rightarrow0}\left( \frac{5}{2} \frac{\sin 5x}{5x} \frac{2x}{\sin 2x}<br />
-\frac{3}{4}\frac{\sin 3x}{3x} \right)<br />

    Now take the limit of both terms and in each term, of all factors.
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