Fall 2005
(Brief Applied Calculus, 3
rd
Edition.
Berresford, Rockett.
Houghton Mifflin, 2004.)
All work should be shown and all answers should be exact unless stated otherwise.
It is fine to leave
radicals in the denominator of a fraction, but they should be reduced.
The departmental formula
sheet and an
acceptable
graphing calculator are the only resources allowed for use during the final
exam.
Each problem on this review sheet is matched with its corresponding objective in the course
outline and the section of the textbook in which it appears.
[Objective #1, Section 2.1]
1.
Evaluate the following limits without using a graphing calculator or making tables.
a.
(
29
+

→
2
1
25
5
lim
t
t
t
b.
x
x
x
x
x
x
+



→
2
2
3
1
6
3
3
lim
c.
2
2
1
1
lim
2


→
x
x
x
[Objective #1, Sections 2.1, 2.7]
2.
Use the given graph to answer the following:
a.
)
(
lim
0
x
f
x
+
→
b.
)
(
lim
0
x
f
x

→
c.
)
(
lim
0
x
f
x
→
d.
xvalues where the function is discontinuous
e.
xvalues where the function is nondifferentiable
f.
xvalues where the slope of the tangent line is zero.
g.
xvalues where the slope of the tangent line is undefined
[Objective #2, Section 2.2]
3.
Use the definition of derivative to find
)
(
'
x
f
.
a.
2
3
2
)
(
2
+

=
x
x
x
f
b.
x
x
f
1
)
(
=
[Objective #2, Sections 2.3, 2.4, 2.6]
4.
Find the equation for the tangent line to the curve of
2
6
3
)
(
2
+

=
x
x
x
f
at the point (0,2).
Write your
answer in slopeintercept form.
5.
Find
dx
dy
for each of the following:
a.
4
2
5
1
2
4
3
x
x
x
x
y
+


=
b.
(
29
1
3
6
3
2
3
4
+
=
x
x
y
c.
(
29
(
29
5
2
1
5
3
2

+

=
x
x
x
y
d.
y=
x
x
x
1
2
3
2
+

e.
1
1
2
+

=
x
x
x
y
f.
3
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 Fall '05
 PamelaSatterfield
 Calculus, Radicals, Supply And Demand, lim, Houghton Mifflin

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