Problem

III. Compute the following:

(a) $\displaystyle \lim_{n\to\infty} a_n$. Here $a_1=\sqrt{6},\ a_2=\sqrt{6+\sqrt{6}},\ a_3=\sqrt{6+\sqrt{6+\sqrt{6}}},\ldots$ $(5\%)$

(b) $\displaystyle \lim_{t\to 0}\left(\int_0^1 (1+x)^t\,dx\right)^{\frac{1}{t}}$. $(10\%)$