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Math Help - limit

  1. #1
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    limit



    hello! who can solve that without using Lhopitals rule

    thank you
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  2. #2
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    Hint:
    \frac{1}<br />
{{\cos (2x)}} = \frac{1}<br />
{{\cos ^2 (x) - \sin ^2 (x)}} = \frac{1}<br />
{{\left[ {\cos (x) - \sin (x)} \right]\left[ {\cos (x) + \sin (x)} \right]}}<br />
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Another approach :

    <br />
\frac{x(1-\tan (x))}{\cos(2x)}=-x\cdot \frac{\tan (x<br />
)-\tan\left(\pi/4 \right)}{x-\frac{\pi}{4}}\cdot \frac{x-\frac{\pi}{4}}{\cos(2x)-\cos(2\pi/4)}

    Now recall that \lim_{x\to a}\frac{f(x)-f(a)}{x-a}=f'(a) and you are done.
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