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MATH 191, Sections 1 and 3
Calculus I
Fall 2007
Practice Exam 1, Solutions
1. (15 points) Find numbers
C
and
a
such that the exponential function
f
(
x
) =
Ca
x
satisﬁes
f
(1) = 2
and
f
(3) = 18.
From
f
(1) = 2 we have
C
·
a
1
= 2, so that
C
=
2
a
. From
f
(3) = 18 we obtain
C
·
a
3
= 18, and
plugging in
C
=
2
a
gives us
2
a
·
a
3
= 18
⇒
2
a
2
= 18
⇒
a
= 3
.
This yields
C
=
2
a
=
2
3
, so our function has the form
f
(
x
) =
C
·
a
x
=
2
3
·
3
x
.
2. (15 points) On a set of axes of your own, draw a graph of
a single function
f
satisfying the
following conditions:
(a)
lim
x
→
2

f
(
x
)
6
=
lim
x
→
2
+
f
(
x
),
(b) lim
x
→
0
f
(
x
) =
∞
,
(c)
f
has a removable discontinuity at
x
= 3.
Since there are myriad possibilities here, come and see me if you’d like me to let you know if your
graph meets the given conditions!
3. (10 points) Explain brieﬂy (and demonstrate!) how to graph the function
H
(
x
) = 2

x

1
 
3
without
a calculator.
In order to obtain the graph of the indicated function, you must begin with the graph of the simpler
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This homework help was uploaded on 04/08/2008 for the course MATH 191 taught by Professor Bahls during the Fall '07 term at UNC Asheville.
 Fall '07
 BAHLS
 Calculus, Exponential Function

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