OpenStudy (kainui):

Why is the limit as you approach infinity of (1+(3/x))^x equal to e^3 and not 1? It looks like as you approach infinity 3/x becomes 0 and 1 to the infinite power is just 1. I know how to do l'hopital's rule, that's not the issue here, I just don't understand why I have to go that route.

6 years ago
OpenStudy (kainui):

\[\lim_{x \rightarrow \infty}[1+(3/x)]^x\] to be clear, this is the limit.

6 years ago
OpenStudy (anonymous):

The answer is e^3

6 years ago
OpenStudy (kainui):

I know the answer, that's not what I'm looking for.

6 years ago
OpenStudy (anonymous):

\[ y=\left(\frac{3}{x}+1\right)^x\\ \ln y = x \ln \left(\frac{3}{x}+1\right) \\ =\frac {\ln \left(\frac{3}{x}+1\right)} {\frac 1 x} \] and apply L'Hospital rule to find that the limit of ln (y) is 3 and conclude.

6 years ago
OpenStudy (kainui):

That didn't answer my question at all.

6 years ago
OpenStudy (anonymous):

\[ 1^\infty \] is undetermined. It is not always equal to 1.

6 years ago
OpenStudy (kainui):

Thanks, that's all I needed.

6 years ago
OpenStudy (anonymous):

With pleasure. I should have read your whole question. It would have saved ne some typing.

6 years ago