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  • Given a real valued function f such that f(x)=<img alt="\left\{\begin{array}{ccc} \frac{\tan ^2\{x\}}{x^2-[x]^2} & \text { for } & x>0 \\ 1 & \text { for } & x=0 \\ \sqrt{\{

Given a real valued function f such that f(x)=\left\{\begin{array}{ccc} \frac{\tan ^2\{x\}}{x^2-[x]^2} & \text { for } & x>0 \\ 1 & \text { for } & x=0 \\ \sqrt{\{x\} \cot \{x\}} & \text { for } & x<0 \end{array}\right. then value of \cot ^{-1}\left(\lim _{x \rightarrow 0} f(x)\right)^2 is

Option: 1

0


Option: 2

1


Option: 3

-1


Option: 4

does not exist


Answers (1)

best_answer

L.H.L. =\sqrt{\cot 1} and R.H.L. =1 and at x=0, f(0)=1 

Hence L.H.L. \neq R.H.L.

Hence limit does not exist

Posted by

Nehul

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