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Solutions for exam 4 of calculus i (math 131) held on december 5, 2008, by l. Ballou. Problems with no calculator and requires showing all work for full credit. Topics covered include integration, definite integrals, derivatives, and area calculations.
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Exam 4-A
L. Ballou Name___________________________
Math 131 Calculus I December 5, 2008
Part 1: No Calculator! Show all work!
(5 points each)
2
2
x x dx x
2
dx
1
x
x
e dx e +
cos sin
x e xdx
2
3 3 1
x dx x +
/ 2 0
sec xdx
π
0
x h x = f t dt
. Give reasons for your
answers.
a. h is a twice-differentiable function of x.
b. h and dh dx are both continuous functions of x.
c. The graph of h has a horizontal tangent at x = 1.
d. h has a local maximum at x = 1
2 v t = t − 2 t − 8
(measured in meters per second).
a. Find the displacement of the particle during the time period 1 ≤ t ≤ 6.
b. Find the total distance traveled during this time period.
3 y = x − x and y = 3 x.
Exam 4-B
L. Ballou Name___________________________
Math 131 Calculus I December 5, 2008
Part 1: No Calculator! Show all work!
(5 points each)
3
3/
x 2 x dx x
3
ln
dx x x
2
dx
Exam 4-B
L. Ballou Name___________________________
Math 131 Calculus I December 5, 2008
Part 2: Show all work for full credit!
2
0
2
0
7 g x dx = 7
1
0
g x dx = 2
, find values of the following:
2
0
g x dx
2
1
g x dx
0
2
f x dx
2
0
2 f x dx
2/
0
g 3 x − 3 f 3 x dx
4
4
g x dx
3
3 1 1
x t G x dt t
2 v t = t − t − 6 (measured
in meters per second).
a. Find the displacement of the particle during the time period 1 ≤ t ≤ 4.
b. Find the total distance traveled during this time period.
0
x g x = f t dt
. Give reasons for
your answers.
a. g is a differentiable function of x.
b. g is a continuous function of x.
c. The graph of g has a horizontal tangent at x = 1.
d. g has a local minimum at x = 1
