calculus - How can you sketch this limit as n approaches infinity?

This was the difficult question on last year's first year differential calculus exam. I thought I was pretty good with limits, but am stumped with this one. I tried multiple ways: first, I used the natural log to pull down the exponent so it became form infinity over infinity, meaning I could use L'Hospital's Rule. The final form, however, was not really helpful for sketching purposes.
After, I tried to use the definition of the derivative, setting t equal to 1/n so the limit would go to zero instead. This, too, yielded a form that was no better than the former; I could not ascertain what x is. I have not yet learned power series or any other such methods; just differentiation.
This is also my first time attempting to use LaTeX, so I'm very sorry if it doesn't come out right. I'll post a picture for backup.

\lim_{n\to \infty} (1+x^(n-1)+x^n)^(1/2)}