3. For the functions below, do the following:
(i) Find the first Taylor Polynomial $T_1(x)$ for $f(x)$ based at $b$.
(ii) Find a bound for the error in approximate the function $f(x)$ by the first Taylor
polynomial $T_1(x)$ for $f(x)$ based at $b$ on the interval $I$.
(iii) Find the second Taylor Polynomial $T_2(x)$ for $f(x)$ based at $b$.
(iv) Find the interval $J$ for the second Taylor polynomial containing $b$ so that the error
is no more than 0.01 on $J$.
(a) $f(x) = \ln(1 - x)$, $b = 0$, $I = [- rac{1}{2}, rac{1}{2}]$
(b) $f(x) = \sin x$, $b = \frac{\pi}{6}$, $I = [- rac{\pi}{4}, rac{\pi}{4}]$
