Math 1550, Practice Final, Fall 2007
Problem 1.
Pick
TWO (2)
of the following 4 problems. Find the
first
derivatives
and
their critical points.
(10 min/20 pts )
(a)
f
(
x
) = 2
x
2
e
1
/x
(b)
f
(
x
) = (2
x
+ 1) ln(2
x
+ 1)
(c)
f
(
x
) = sin
x
2 sin
x
+ 3
3
(d)
f
(
x
) =
x
2
+ 4
x

11
x
+ 5
Problem 2.
Pick
TWO (2)
of the following 4 problems.
Evaluate the integrals.
[10mts, 20pts]
(a)
e
x
e
e
x
cos(
e
e
x
)
dx
(b)
π/
4

π/
4
cos
x
sin
x
sin
2
x
+ 2
dx
(c)
10

10
2 +
x
(4
x
2
+ 1)
3
dx
(d)
6
x
(3
x
+ 1)
2
dx
Problem 3.
Pick
ONE (1)
of the following two problems.
(5 min/20 pts)
(a)
Discuss the function (even, odd, lim
x
→±∞
f
(
x
), vertical asymptotes, intercepts,
increasing, decreasing, maxima and minima, concave up, concave down, points of
inflection, and finally a sketch of the graph). Show all work.
f
(
x
) =
1

2
x
x
10
f
(
x
) =
5

9
x
2
x
9
f
(
x
) =
10(11

18
x
)
x
12
.
(b)
Set up integrals (first using vertical slices and then with horizontal slices) for the
volume of the solid obtained by rotating the region bounded by curves
y
= 2
x
,
x
= 3, and
y
= 0 about the axis
y
= 6. Do
not
evaluate the integrals.
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 Fall '08
 Wei
 Calculus, Critical Point, Derivative, Continuous function, average position, following ﬁve problems, left endpoint rule, endpoint rule R3

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