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Evaluate the limit . underset(n to 00)...

Evaluate the limit .
`underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))………(1+(n^(2))/(n^(2)))]^(1/n)`

A

`(2)/(e^(2))e^(pi//2)`

B

`(e^(2))/(2)e^(pi//2)`

C

`(2)/(e^(pi//2))e^(2)`

D

`(e^(pi//2))/(2e^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
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