MATH 131:100 Exam #3
Instructor: Keaton Hamm
June 30, 2014
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“An Aggie does not lie, cheat or steal or tolerate those who do.”
Instructions:
ˆYou MUST clear all memory on your calculator: to do this hit 2nd, then +
(MEM), then Reset (7), move the cursor over to the right ALL, select All Memory
(1), then Reset (2)
ˆShow your work for each work out problem clearly and legibly. Box your final
answer in the work out problems.
ˆPoint values are shown for each problem.
ˆYou may use a TI-83, TI-84, or TI-Nspire nonCAS version for all problems. Other
calculators are not permitted.
ˆIf you need extra scratch paper, ask me and I will provide you with some.
ˆYour grade will be written on the final page of the exam.
ˆThere should be 8 pages with problems numbered 1-17 on this exam. There are
100 possible points.
Good Luck!
Section 1: Definitions
Give the mathematical definition for each of the following terms or concepts. (Each
problem is worth 4 Points)
1) State the Fundamental Theorem of Calculus
2) A number c is a Critical Point of a funciton f if
3) State the Mean Value Theorem
4) We say that f (c) is an absolute maximum of f if
Section 2: Graphical Concepts
5) (12
Z xPoints, 2 each) The following is the graph of the function y = f (t). Let
f (t)dt.
g(x) =
0
y
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01
a) Evaluate g(0)
b) Evaluate g(2)
c) Evaluate g(6)
d) Where is g increasing?
e) Where is g decreasing?
f ) Where does g have a local maximum value?
Section 3: Work Out Problems
6) (6 Points) If
f 00 (x) = x2 + 3 cos x
f (0) = 2 and f 0 (0) = 3. Find the formula for f (x).
7) (5 Points) Suppose that f is a continuous function on [1, 10], and that
f (1) = 5, f (10) = 7, f 0 (1) = 2, and f 0 (10) = 8. Evaluate
Z 10
f 0 (x)dx
1
20
Z
Z
30
f (x)dx = 5,
8) (5 Points) Suppose that
10
Then evaluate
Z
Z
f (x)dx = 6, and
20
30
[3f (x) − 4g(x)] dx
10
9) (6 Points) Evaluate
Z
x2 + 3x − 1
dx
x2
10) (6 Points) Evaluate
Z 30
√
1
3
+ 2x − x dx
x
g(x)dx = 2.
10
11) (6 Points) If
Z
x3
g(x) =
2x2
t2 − 1
dt
t+7
0
Find g (x).
12) (5 Points) Evaluate
Z
(ln x)2
dx
x
13) (3 Points) Evaluate
Z
2
−2
x + x3 − 5x7
dx
x2 + 2
14) (6 Points) Find the absolute maximum and minimum of the function
f (x) = −x2 + 4x − 3
on the interval [0, 4].
15) (6 Points) Evaluate
Z
x2 (x3 + 5)9 dx
16) (10 Points) A rectangular box with an open top has a square base, and is made
from 48 ft2 of material. What dimensions will result in a box with the largest possible
volume?
17) (8 Points) Find two nonnegative numbers whose sum is 9 and so that the
product of one number and the square of the other number is a maximum.
Final Score: