What is the lim x->0 (1+3x) ^ (1/x)

You can solve this using the definition of e: this might help you:

Exponentiation - Wikipedia, the free encyclopedia

Think of n as used on this site as 1/x in your problem (i.e, this site talks about the limit as n approaches infinity, whereas you want the limit as x approaches 0). You'll see that your problem reduces to a power of e. Can you take it from here?

Can you use L'Hopital's method? Is that a legal move?

No, L'Hopital is probably not the best to tackle this one.

Use the fact that

Let t=3x and x=t/3.





Now, see what you get as the limit?

Oh wow that's so much simpler. I used L'Hopital... still got the same answer but wow nty version was so much more complicated. Thank you very much!