Saturday, April 14, 2018

limits - Find: $ lim_{xto frac{pi}{4}} frac{sin 4x}{1-sqrt{2} cos x}$ (no L'Hopital)


Find: $\displaystyle \lim_{x\to \frac{\pi}{4}} \frac{\sin 4x}{1-\sqrt{2} \cos x}$ (no L'Hopital)



By L'Hopital it is easy to show that this limit is $-4$. But I'm not finding the right approach to prove without using it.



Hints and answers appreciated. Sorry if this is a duplicate.

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