Question 1

Consider the function f(x) = e^-x/2.cos(x). Compute the Taylor polynomials

T2(x), T3(x) and T4(x) of degrees 2,3,4 about x = 0 in Maple and graph the differences f(x)

-T2(x), f(x) - T3(x) and f(x) — T4(x) for 0≤x≤2 on the same plot. The differences

tell us the error of the Taylor polynomial as an approximation to f(x). To get a Taylor polynomial

see ?taylor

Use Maple to calculate (1) the maximum error and (ii) the average error of

T2(x), T3 (x) and 74(x) on the interval 0 ≤ x ≤ 2. What is the average value of a function

g(x) on an interval a ≤x≤ b you ask? See Section 6.5 of the Stewart Calculus text or look it up on

the web.