Chap 1.3, pp. 47-49: #26, 58, 62

Chap 1.6, pp 73-74: #2, 32

Chap. 2.5, p. 131: #6, 12, 16

Chap. 2.7, p. 154: #2, 3 (explain!), 8, 12, 18

Chap. 3.5, p. 221: #1,4 (be sure to identify what g(x) and f(u) are)

#8, 15, 34, 36, 55 (explain how you did it), 64

Note: you could look at COW problems on the Chain Rule for some practice with immediate help.

Chap. 3.6, p. 230: #23, 24

Chap. 3.10, p. 257-8: #16, 27

Chap. 4.1, p. 285: #50, 68(b)

Chap. 4.7, p. 335: #17, 20

Chap. 4.7, p. 335: #6, 7, 8

Chap. 4.10, p. 356-7: #1, 2, 53, 54

PRACTICE EXAM

PRACTICE EXAM SOLUTION

Figure 6a

Figure 6b

Use COW->Book II->Integration->Sums->Riemann Sums, Problem 2: Make Riemann sum approximations to the integral of sin(x) from 0 to PI. Use 5, 10, and 15 subintervals. Try all methods of choosing where to evaluate sin(x) in the little subintervals, and notice in the pictures how these different choices look. Sketch a few representative examples, and explain their appearance. Give the values of the Riemann sums for the Upper Riemann Sum (too big) and the Lower Riemann Sum (too small). Suppose for each choice of N you average these two values -- is it closer to the actual value (which is 2)? Do the same thing with left endpoint and right endpoint Riemann sums. Does it help to average these two?

Chap. 5.1, p. 376-7: #11, 12

Chap. 5.2, p. 388-9: #9, 12, 31, 32

Chap. 6.2, pp. 448-449: #1, 2, 3, 23, 24

Chap. 6.3, p. 454: #1, 2

Chap. 6.5, p. 462: #1, 2