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If  \mathrm{f(x)=(x+1)^{\cot x}}   be continuous at x=0, then f(0) is equal to

Option: 1

0


Option: 2

1/ e


Option: 3

e


Option: 4

none of these


Answers (1)

best_answer

 For f(x) to be continuous at x=0, we must have

\mathrm{ \lim _{x \rightarrow 0}(1+x)^{\cot x}=f(0) \Rightarrow e^{\lim ^{10} x \cos x}=f(0) \\ }

\mathrm{ \Rightarrow c^{\lim _{x \rightarrow 1} \frac{x}{\operatorname{Lin} x}}=f(0) \Rightarrow e^{\prime}=f(0) \\ }.

Posted by

himanshu.meshram

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