Please help me this,
estimate the value of the limit
lim x-0 (1+x)^1/x

Question

Please help me this,
estimate the value of the limit
lim x->0 (1+x)^1/x

anonymous · Answer

$$\lim_{x \rightarrow 0} (1+x)^{1/x}$$
is the answer 0?

geerky42 · Answer

We can let $\large L = (1+x)^{1/x} = e^{\ln L}$, 

So   $\Large \displaystyle \lim_{x\rightarrow0}L = \lim_{x\rightarrow0}e^{\ln L} = \lim_{x\rightarrow0}e^{\frac{\ln(1+x)}{x}} =e^{\lim_{x\rightarrow 0}\frac{\ln(1+x)}{x}}$

After direct substitution, you will get indeterminate form: 0/0, so apply L'Hopital's rule. I'm sure you can handle it on your own afterward.

Hope this helps!

geerky42 · Answer

Does this help? Need me to clarify more? @gogonhan

anonymous · Answer

can you please show more work, i dont get it... Sorry I just got Caculous this morning... so a lot of confusing...

geerky42 · Answer

which part are you confused with?

anonymous · Answer

okie... I got it... just read the book... thank you :D

geerky42 · Answer

no problem!