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If f(n)=int(0)^(2015)(e^(x))/(1+x^(n))dx...

If `f(n)=int_(0)^(2015)(e^(x))/(1+x^(n))dx`, then find the value of `lim_(nto oo)f(n)`

A

`e-1`

B

`e`

C

`1`

D

`e^(2)-1`

Text Solution

Verified by Experts

The correct Answer is:
A
`=int_(0)^(1)lim_(nrarroo)((e^(x))/(1+x^(n)))dx+int_(1)^(2015)lim_(nrarroo)(e^(x))/((1+x^(n)))dx`
`=int_(0)^(1)e^(x)dx+0=e-1`
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