InterviewSolution
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InterviewSolution
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The value of `lim_(xrarr0) ((1+x)^(1//x)-e)/(x)` isA. 1B. `(e)/(2)`C. `-(e)/(2)`D. `(2)/(e)` |
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Answer» Correct Answer - C We have , `(1+x)^(1//x)=e(log(1+x))/(x)=e(1)/(x)(x-(x^2)/(2)+(x^3)/(3)-...)` `rArr (1+x)^(1//x)=e^(1-(x)/(2)+(x^3)/(3) -..)= e.e (-x)/(2)+(x^2)/(3).....` `lim_(xto0)((1+x)^(1//x)-e)/(x)lim_(xto0)(e.e^(-(x)/2)+(x^2)/(3)....._(-e))/(x)` `e lim_(xto0) ({e^(-x//2+x^2//3+....)-1})/((-(x)/(2)+(x^2)/(3)+....))xx((-(x)/(2)+(x^2)/(x)+....))/(x)=-(1)/(2)e` |
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