# MATH 131:100 Exam #3 Instructor: Keaton Hamm June 30, 2014

```MATH 131:100 Exam #3
Instructor: Keaton Hamm
June 30, 2014
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First Name:
Signature:
“An Aggie does not lie, cheat or steal or tolerate those who do.”
Instructions:
You 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)
Show your work for each work out problem clearly and legibly. Box your final
answer in the work out problems.
Point values are shown for each problem.
You may use a TI-83, TI-84, or TI-Nspire nonCAS version for all problems. Other
calculators are not permitted.
If you need extra scratch paper, ask me and I will provide you with some.
Your grade will be written on the final page of the exam.
There 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:
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