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  • How to find   <img alt="\mathrm{\lim (\tan x)^{\tan (2 x)}, x \rightarrow \pi / 2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20%28%5Ctan%20x%29%5E%7B%5Ctan%

How to find   \mathrm{\lim (\tan x)^{\tan (2 x)}, x \rightarrow \pi / 2}

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

5


Answers (1)

best_answer

Calculate first the easier limit

                                 \mathrm{\lim _{x \rightarrow \frac{\pi}{2}}(1+\tan (x))^{\frac{1}{\operatorname{lan}(x)}}=1}

Then do you have the expression 

                    \mathrm{(1+\tan (x))^{\tan (2 x)}=(1+\tan (x))^{\frac{\tan (x)}{\tan (x)} \tan (2 x)}=(1+\tan (x))^{\frac{1}{\operatorname{con}(x)} \cdot \frac{2 \tan ^2(x)}{1-\tan ^2(x)}}}

Verify now that

                                 \mathrm{\lim _{x \rightarrow \frac{\pi}{2}} \frac{2 \tan ^2(x)}{1-\tan ^2(x)}=-2}

Your limit is equal to \mathrm{1^{-2}=1}

Posted by

SANGALDEEP SINGH

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