Let n 5 and use a calculator to compute

Question

Suppose f is defined by f(x) = 3e^{(cos x)}. Maple produced graphs of f and its first four derivatives on the interval [2, 7] (be careful when examining the derivative graphs - look carefully at the vertical scales!). The graph of f is below, and the graphs of the first four derivatives of f are on the back of this page. You should assume that the graphs are correct for this problem.

Suppose I  is the value of

₂∫⁷f(x) dx

a) Use the graph of f alone to estimate I.

b) Use the information in the graphs to tell how many subdivisions N are needed so that the Trapezoid Rule approximation T_N will approximate I with error < 10^(-5).

c) Use the information in the graphs to tell how many subdivisions N are needed so that the Simpson's Rule approximation S_N will approximate I with error < 10^(-5) .

d) Let N = 5 and use a calculator to compute y₀,···, y_N for the Trapezoid Rule up to 3 decimal places. Compute an approximation of I with the Trapezoid Rule for N = 5. Compare it with your result for part a).