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lim( x to (pi/(2)) (tan2x)/(x-(pi)/(2))...

`lim_( x to (pi/(2)) (tan2x)/(x-(pi)/(2))`

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To solve the limit \( \lim_{x \to \frac{\pi}{2}} \frac{\tan(2x)}{x - \frac{\pi}{2}} \), we will follow these steps: ### Step 1: Substitute \( x = \frac{\pi}{2} + h \) Let \( h = x - \frac{\pi}{2} \). Then as \( x \to \frac{\pi}{2} \), \( h \to 0 \). Thus, we can rewrite \( x \) in terms of \( h \): \[ x = h + \frac{\pi}{2} \] ...
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