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Let f(x) = {{:((x)/(sin x) ",",x in "(...

Let
`f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):}`
Consider the integral
`I_(n) = sqrt(n)int_(0)^(1//n) f(x)e^(-n x)dx`.
Then `lim_(n rarr infty) I_(n)`

A

does not exist

B

exists and is 0

C

exists and is 1

D

exists and is `1 – e^(–1)`

Text Solution

Verified by Experts

The correct Answer is:
B
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