Higher order polynomimals:

Find $T_4(x)$ at $b = 4$ for $f(x) = x^8-1$.

Find the third degree Taylor polynomial of $f(x) = \sqrt{x}$ at $b = 3$

Taylor series and radius of convergence:

For the following, find the Taylor series at the given base and give the interval on which it converges.

• $\frac{1}{1-x}$ at $b = 0$
• $\tan x$ at $b = 0$
• $\cos (x - \pi/6)$ at $b = \pi/6$
• $\frac{1}{3-2x}$ at $b = 2$