MATH 272, Spring 2016, Test 1
1. A tank of water, = 62.4, is in the shape of a cone (point down) with height 5 feet
and radius 2 feet. It is filled to the top with water. Find the work needed to pump
all but 1 foot of water to the top (and the out) of the
MAT 271, Review for Test #2
3.1 3.6
1. Differentiate and simplify:
3x
2
a. y 2
b. y x (3x 1)
c. f ( x)
d. y x sec x 2 tan x
x 1
2x x 2
4
x2 9
e. f ( x)
f. y csc 2 cot 2 g. s(t ) sec t
h. y x 3 sin 2 x
2
4 x
x
l. y 1 cos x
j. f ( ) sin 2 k. y
1 c
Calculus II
Test 2
June 9, 2015
1. Find
R
ln(x)
dx.
x2
2. Find
R
e3x cos(x)dx. (15pt.)
(5pt.)
1
3. Find
R
sin2 (x)cos3 (x)dx. (10pt.)
4. Find
R
1
dx.
x2 16x2
(15pt.)
5. What does it mean for a rational function to be proper? (5pt.)
2
6. Find
R
x3 x
dx.
x2
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