Friday, 24 November 2017

real analysis - Compute limlimitsxto0+efrac1sqrtxcdot(1sqrtx)frac1x

Evaluate limx0+e1x(1x)1x


I tried using limx0(1+x)1x=e
like so:
l=limx0+e1x[(1+(x))1x]1x=limx0+e1x1x=e0=1

However, the right answer is 1e. Why is it that the whole expression in square brackets can't be taken as e in this case?

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