Problem 420 (difficulty: 2/10)

Find a good \(\displaystyle \delta\) or \(\displaystyle L\) for \(\displaystyle \varepsilon >0\) or for \(\displaystyle K\) for the following functions.

 (1)  \(\displaystyle \lim\limits_{x\to 1+}(x^2+1)/(x-1),\)      (2)  \(\displaystyle \lim\limits_{x\to \infty}\frac{\sin(x)}{\sqrt x}\).

Give me another random problem!