MAC 2311
AM April 24, 2009
Final Exam
Prof. S. Hudson
1) (10 pts) Compute
y
0
;
a)
y
= (2
x
)
x
b)
y
= log
3
(2
x
+ 1)
2) (10 pts) Solve this Initial Value Problem:
y
0
(
t
) =
e
t
+
t
and
y
(0) = 2.
3) (25 pts) Compute and simplify;
R
e
2
x
dx
=
R
t
1+16
t
2
dt
=
R
1

2
t
3
t
3
dt
=
R
cos
2
(
x
)
dx
=
R
tan
2
(
x
)
dx
=
4a) (10 pts) Find the slope of the tangent line to the curve,
x
=
√
t
,
y
= 2
t
+1
at
t
= 1. For maximum credit, use the chain rule as done in class.
4b) (5 pts) For the same curve as above, find
d
2
y/dx
2
when
t
= 1.
5) (10 pts) Sketch a graph of
y
=
x
2

1
x
3
. Find all critical points, inflection
points and asymptotes [and label them clearly]. You may use:
y
0
=
3

x
2
x
4
y
00
=
2(
x
2

6)
x
5
√
3
≈
1
.
8
√
6
≈
2
.
4
1
.
8

3
≈
0
.
18
2
.
4

3
≈
0
.
07
1
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6) (20 pts) Answer TRUE or FALSE:
f
(
x
) = ln

x

is an increasing function.
A rational function is continuous except where the denominator is zero.
The function cot(
x
) is continuous on the interval (

π/
4
, π/
4).
If
f
is a polynomial, then it has exactly one antiderivative whose graph
contains the origin.
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 Spring '08
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 Calculus, Derivative, pts, Limit of a function, Prof. S. Hudson

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