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If f(x)=1/(1+e^(-1 /x)) ,x!=0 and 0,x=0...

If `f(x)=1/(1+e^(-1 /x)) ,x!=0 ` and 0,x=0 then at x=0 (A) right hand limit of f(x) exists but not left-hand limit (B) left-hand limit of f(x) exists but not right- hand limit (C) both limits exists but are not equal (D) both limits exist and are equal

Text Solution

Verified by Experts

LHL=`lim_(x->0-)(1/(1+e^(-1/x)))`
`=lim_(h-.0)(1/(1+e^(1/h)))`
`=0`
RHL=`lim_(x->0+)1/(1+e^(-1/x))`
`=lim_(h->0)1/(1+e^(-1/h)`
`=1/(1+0)`
LHL`!=`RHL
option c is correct.
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