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Math 112
Review Exercises for the Final Exam
The following are review exercises for the Math 112 final exam. These exercises
are provided for you to practice or test yourself for readiness for the final exam. There are
many more problems appearing here than would be on the final. These exercises
represent many of the types of problems you would be expected to solve on the final, but
are not meant to represent all possible types of problems that could appear on the final
exam.
Your final exam will be in two parts: the first part does not allow the use of a
calculator, and the second part does allow the use of a graphing calculator.
Since the
exercises in this review sheet are mixed together, we have put a
symbol next to
exercises or parts of exercises where you WILL be allowed to use the graphing
calculator: otherwise you should be able to solve the problem WITHOUT a calculator.
Such a symbol will not be on the final exam. Please note that for the final, you may use
any graphing calculator except
the TI89, TIInspire, and any calculator with a QWERTY
keypad.
Show all your work: unsupported results may not receive credit.
1.
Sketch the graph of the following:
Using interval notation, state the domain and the range. State the equation(s) of the
asymptote(s). Find the x and yintercepts where they exist.
(a)
4
3
)
(
2
+
=
−
x
x
f
(b)
3
)
2
ln(
)
(
+
−
=
x
x
f
(c)
1
5
)
(
3
+
=
−
x
x
f
(d)
2
)
1
log(
)
(
+
−
=
x
x
f
2.
Given
3
.
2
5
log
=
a
and
6
.
1
3
log
=
a
, fill in the table below with the appropriate values.
X
15
9
3
5
5a
2
3
a
x
a
log
3.
Which is the following is larger:
28
log
3
or
63
log
4
?
JUSTIFY YOUR ANSWER
FOR CREDIT
4.
Find the EXACT solution for the following:
(a)
3
)
log(
)
2
log(
=
−
+
x
x
(b)
)
log(
1
)
3
log(
x
x
−
=
−
(c)
x
x
3
1
2
8
2
=
+
(d)
3
3
2
27
3
+
−
=
x
x
(e)
0
2
2
=
−
x
x
e
e
x
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5.
Given the following equations: Find (i) all solutions in the interval
)
2
,
0
[
π
in radians,
and (ii) all solutions in radians:
(a)
0
2)
)(sin
3
(2sin
=
−
−
x
x
(b)
0
3

sin
2sin
2
=
+
x
x
(c)
0
1

tan
2
=
x
6.
Solve for
x
accurate to 2 places if
x
is in the interval
)
(0,
:
)
2
ln(
)
4
sin(
+
=
x
x
.
7.
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 Fall '10
 stern
 Trigonometry, Sin, Cos, Periodic function

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