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underset(xtooo)lim(e^(1//x^(2))-1)/(2tan...

`underset(xtooo)lim(e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi)` is equal to

A

`-1/4`

B

`-1/2`

C

`1/2`

D

Does not exists

Text Solution

Verified by Experts

The correct Answer is:
B
`lim_(xrarroo) (e^(1/(x^(2)))-1)/(2tan^(-1)(x^(2))-pi)=lim_(xrarroo) (e^(1/(x^(2)))-1)/(2((pi)/2-cot^(-1)x^(2))-pi)`
`lim_(xraroo)=(e^(1/(x^(2)))-1)/(-2tan^(-1)1/(x^(2)))=-1/2`
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