Question

please answer those two questions.....

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Answer 1

Answer:

$lim_{x \to0}( \frac{ \sin(\pi - \pi \cos {}^{2} (x) ) }{ {x}^{2} } ) \\ = lim_{x \to0} \frac{ \sin(\pi(1 - \cos {}^{2} (x) ) }{ {x}^{2} } \\ = lim_{x \to0} \frac{ \sin(\pi \sin {}^{2} (x) ) }{ {x}^{2} } \times \frac{\pi \sin {}^{2} (x)}{\pi \sin {}^{2} (x) }$

All right here is very cool trick i used to solve limit if you don't know . whatever in sin function any complex function or anything if it is going for zero and there is same function in denominator so it will be 1 .

So your limit becomes

$lim_{x \to0} \frac{\pi \sin {}^{2} x}{ {x}^{2} } = \pi$