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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 |
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Answer» 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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