{[(1+x)/^1/x]/e}1/x极限,x趋近于0

题目

{[(1+x)/^1/x]/e}1/x极限,x趋近于0

答案

f(x) = {[(1+x)/^(1/x)]/e} ^(1/x)ln f(x) = (1/x) [ (1/x) ln(1+x) - 1] = [ ln(1+x) - x] / x²lim(x->0) lnf(x) = lim(x->0) [ ln(1+x) - x] / x²= lim(x->0) [1/(1+x) - 1] / (2x)= -1/2原式 = e^(-1/2...