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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 TN 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 SN will approximate I with error < 10(-5) .
d) Let N = 5 and use a calculator to compute y0,···, yN 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).
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