How do I find the limit of (1+sin(pi times x))^(1/x) as x approaches 0? I tried using wolframalpha, but am unable to understand their steps. My thinking is that you set y=the limit and use L'hopital's rule a couple times. The answer I got was y=e^0---y=1, but the answer isn't right.

Question

How do I find the limit of (1+sin(pi times x))^(1/x) as x approaches 0? I tried using wolframalpha, but am unable to understand their steps. My thinking is that you set y=the limit and use L'hopital's rule a couple times. The answer I got was y=e^0--->y=1, but the answer isn't right.

Thanks a ton in advance!

Steve · Answer

The steps on wolframalpha looked pretty clear to me. There was a lot of formal shifting of limit of product as product of limits, etc, but they basically used

lim sinx/x = 1 as x->0

lim sin(pi*x) / (pi*x)/pi = pi