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Let f(x)=\left\{\begin{array}{ll}x^{2}-1 , 0<x<2 \\ x+1 , 2 \leq x<3\end{array}\right.. Then

Option: 1

lim _{x \rightarrow 2}\, \, f(x) exists


Option: 2

f is not continuous at 2


Option: 3

f is continuous at 2


Option: 4

none of these


Answers (1)

best_answer

\lim _{x \rightarrow 2-} f(x)=3, \lim _{x \rightarrow 2+} f(x)=3, f(2)=3.. Hence (a) and (b) are true. 

Further f^{\prime}(x)=\left\{\begin{array}{ll}2 x & , 0<x<2 \\ 1 & , 2<x<3\end{array}\right..

Hence f^{\prime}(2-)=4, f^{\prime}(2+)=1.

Thus f is not differentiable at 2 .

 

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manish

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