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If f(x)=(x+1)^(cotx) is continuous at x=...

If `f(x)=(x+1)^(cotx)` is continuous at x=0, then what is f(0) equal to?

A

0

B

`-e`

C

`e`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(xto0)(1+x)^(cotx)=lim_(xto0)((1+x)^(1//x))^(x cotx)`
`=lim_(x to0)(e^x cot x)=e`
Since `f(x)` is continuous at `x=0`
`:.f(0)=lim_(xto0)f(x)=e`
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