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The function defined by f(x)={((x^(2)+...

The function defined by
`f(x)={((x^(2)+e^((1)/(2-x)))^(-1)",",x ne 2),(k" ,",x =2):}` is continuous from right at the point x =2, then k is equal to

A

0

B

`(1)/(4)`

C

`-(1)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since, `lim_(x to 2^(+)) f(x)=f(2)=k`
`rArr k =lim_(h to 0) f(2+h)`
`rArr k=lim_(h to 0)[(2+h)^(2)+e^((1)/(2-(2+h)))]^(-1)`
`therefore =lim_(h to 0)[4 +h^(2)+4h+e^(-1//h)]^(-1)=(1)/(4)`
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