Question

Evaluate the given limit :

$lim _{x - - - > \frac{\pi}{2} }( \frac{ \tan2x }{x - \frac{\pi}{2} } )$
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Answer 1

Given

$lim \: x--> \frac{\pi}{2} ( \frac{ \tan(2x) }{x - \frac{\pi}{2} } )$

the given form is indeterminate form so using L - Hospital rule

differentiating fraction above and below with respect to X we get

$lim \: x--> \frac{\pi}{2} (\frac{2 { \sec(2x) }^{2} }{1} )$

Now

Sec π = - 1

src^2 π = 1

so

2 is the answer

Answer 2

Answer:

Given

$$\begin{lgathered}lim \: x--> \frac{\pi}{2} ( \frac{ \tan(2x) }{x - \frac{\pi}{2} } ) \\\end{lgathered}$$

the given form is indeterminate form so using L - Hospital rule

differentiating fraction above and below with respect to X we get

$$\begin{lgathered}lim \: x--> \frac{\pi}{2} (\frac{2 { \sec(2x) }^{2} }{1} ) \\\end{lgathered}$$

Now

Sec π = - 1

src^2 π = 1

so

2 is the answer