Question

Evaluate the following limit :
$\ \textless \ br /\ \textgreater \ \qquad\large\sf{\leadsto \quad\lim_{x\to \frac{\pi}{2}}\dfrac{tan~2x}{x-\dfrac{\pi}{2}}}$

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Answer 1

Answer:

$lim_{x \to \: \frac{\pi}{2} } \frac{ \tan2x}{x - \frac{\pi}{2} }$

Apply L'hopital's rule

$= lim_{x \to \: \frac{\pi}{2} } \frac{ {sec}^{2}(2x) \times 2 }{1}$

Plug in the value

x=pi/2

$= \frac{ {sec}^{2}(2 \times \frac{\pi}{2}) \times 2 }{1} \\ \\ \sf \blue {\underline{simplify}} \\ \\ = 2$

2 is the answer!

Answer 2

Step-by-step explanation:

$refer \: \: the \: \: attachment$

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