InterviewSolution
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InterviewSolution
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`lim_(xrarr0)(e^(1//x)-1)/(e^(1//x)+1)`,isA. -1B. 1C. 0D. non-existent |
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Answer» Correct Answer - D Let `f(x)(e^1//x-1)/(e^(1//x)+1)`.Then, (LHL of `f(x)` at `x=0`) ` =lim_(xto0^-)f(x) =lim_(hto0) f(0-h)=lim_(hto0) (e^1//x-1)/(e^(-1//x)+1)` `=lim_(hto0) (((1)/(e^(1//h))-1)/((1)/(e^(1//h))+1))=-1[e^(1//h)to oo rArr (1)/(e^(1//h))to0]` and, ` [RHL of ` f(x)` at `x=0`] `=lim_(xto0^+) f(x) =lim_(hto0) f(0+h)=lim_(hto0) (e^(1//h)-1)/(e^(1//h)+1)` `lim_(hto0)(((1)/(e^(1//h))-1)/(1+e^(1//h)))["Dividing Nr and by "e^(1//h)]` Clearly, `lim_(xto0^-) f(x)ne lim_(xto0^+)f(x)`. Hence, `lim_(xto0) f(x)` does not exist. |
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