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  • Given a real valued function f such that <img alt="f(x)=\left\{\begin{array}{

Given a real valued function f such that f(x)=\left\{\begin{array}{cll}\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 the 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 \mathrm{x}=0, \mathrm{f}(0)=1

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

Hence limit does not exist

Posted by

Sanket Gandhi

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