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In order that the function f(x)=(x+1)^(c...

In order that the function `f(x)=(x+1)^(cotx)` is continuous at x = 0, the value of f(0) must be defined as

A

`f(0)=(1)/(e )`

B

`f(0)=0`

C

`f(0)=e`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, `f(0) =lim_(x to 0) f(x) =lim_( x to 0) (x+1)^(cot x)`
`=[lim_(x to 0) (1+x)^((1)/(x))]^(x cot x)`
` =e^((lim_( x to0) (x)/(tan x))) =e^(1)=e`
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