I need to evaluate the following limits:

1)$\displaystyle \lim_{x\to0} (\sqrt{x+1})/x$, where $\displaystyle (x>-1)$

2)$\displaystyle \lim_{x\to\infty} (\sqrt{x+1})/x$, where $\displaystyle (x>0)$

here is what I have so far

$\displaystyle (\sqrt{x+1})/x = \sqrt{\frac{x+1}{x^2}} = \sqrt{\frac{1}{x} + \frac{1}{x^2}} < \sqrt{\frac{2}{x}}$ . . . I don't know if I'm on the right track or not. Any help is greatly appreciated,thanks