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Question
\[\lim_{x \to \frac{\pi}{2}} \frac{\sin 2x}{\cos x}\]
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Solution
\[\lim_{x \to \frac{\pi}{2}} \frac{\sin 2x}{\cos x} \left[ \sin 2x = 2 \sin x \cos x \right]\]
\[ = \lim_{x \to \frac{\pi}{2}} \frac{2 \sin x \cos x}{\cos x}\]
\[ = \lim_{x \to \frac{\pi}{2}} 2 \sin x\]
\[ \Rightarrow 2\]
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