Calculus I, Departmental Final Exam Review
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This review should be used as a guide only.
These problems are intended to represent
the types
of
skills that you should have mastered in Calculus I. The final exam will require you to show mastery of
these same skills, but through different problems.
A successful Calculus student should be able to
recognize the problem type and proceed in a methodical manner to a solution rather than memorize how
to work a PARTICULAR problem.
Part I—Limits and Continuity and Applications
1.
Use the given graph to answer questions a – g
2.
Evaluate the following limits analytically (do not use a table or a graph).
Give
exact answers.
(Sections 2.3 – 2.4)
a.
(
)
x
e
x
x
π
sin
lim
0
−
→
b.
x
x
x
2
2
lim
0
−
+
→
c.
2
2
1
1
lim
2
−
−
→
x
x
x
d.
x
x
x
3
sin
2
lim
0
→
e.
)
1
2
(ln
lim
3
2
+
+
→
x
x
e
x
f.
1
1
lim
2
0
−
−
→
x
x
x
e
e
g.
)
(
lim
1
x
f
x
+
→
where
⎩
⎨
⎧
>
+
≤
=
1
,
1
1
,
)
(
2
x
x
x
x
x
f
h.
2
2
lim
2
−
−
−
→
x
x
x
i.
3.
Find the x-values (if any) at which
f
is not continuous.
Identify any discontinuities as removable
or non-removable.
(Section 2.4)
a)
10
3
2
)
(
2
−
−
+
=
x
x
x
x
f
b)
⎩
⎨
⎧
<
−
≥
+
=
0
,
1
0
),
1
ln(
)
(
2
x
x
x
x
x
f
4.
Find any vertical asymptotes for a)
1
1
2
+
−
=
x
x
y
b)
1
1
2
−
−
=
x
x
y

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