a) In lectures we derived an expression for the Maclaurin polynomial for cos(x). Use Taylor's theorem to estimate how many terms need to be used to approximate cos(2) to within 0.001. (Hint: For f(n+1(z), think about what y-values cos(x) and sin(x) are both bounded by. You'll need to use some trial and error to nd n once you have a bound for the remainder.)

b) Find the Taylor series for f(x) = ln(x), centred at a = 3, along with its interval of convergence.