# Can someone show me how to evaluate lim x->0+ (1+X)^(1/x) using L'Hopital's rule? I know I need to convert it into proper form, a fraction I think, to solve it. I think it has something to do with...

Can someone show me how to evaluate lim x->0+ (1+X)^(1/x) using L'Hopital's rule?

I know I need to convert it into proper form, a fraction I think, to solve it. I think it has something to do with logarithms but I can't figure it out. Thanks!

sciencesolve | Certified Educator

calendarEducator since 2011

starTop subjects are Math, Science, and Business

You need to take the logarithm of the limit such that:

`ln lim _(x->0) (1+x)^(1/x) = lim_(x->0) ln ((1+x)^(1/x))`

Using logarithmic identity yields:

`lim_(x->0) ln ((1+x)^(1/x)) = lim_(x->0) (1/x)ln (1+x)`

`lim_(x->0) (1/x)ln (1+x) = lim_(x->0) (ln...

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