Practice Test #1
–
MAC2312
Directions:
Use this practice test as a guide for your study for Test #1. This exam is
not
comprehensive, so study your quiz, class notes and homework problems in addition to
completing this exam. Solutions are posted on the course websit
e under “Solutions”.
1)
Use hyperbolic function identities (not definitions) to prove that
1
)
(
csc
)
(
coth
2
2
x
h
x
.Start on one side and do one step at a time to show equivalence to
the other side.
2)
For the function
3
)
2
sinh(
ln
6
)
(
x
x
f
, find
)
(
x
f
dx
d
. Simplify completely.
3)
Find the indefinite integral
dx
x
5
4
9
2
. (Hint: Use a formula from Section 5.9).
4)
Find the area between
1
4
)
(
2
x
x
x
f
and
1
)
(
x
x
g
by doing the following:
a) Sketch both functions on the same coordinate axes.
b) Find the xvalues where the functions intersect.
c) Find the area of the region(s).
5) Find the area of the region bounded by
2
5
y
x
and
3
y
x
by doing the following:
a) Sketch both graphs on the same coordinate axes.
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 Fall '11
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