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31L Test #
"
(Tomberg, spring 09)
Name:_______________________________
I reaffirm the Duke Community Standard.
You must clearly show all your work on each problem to receive full credit. Unsupported work may
receive no credit
.
1.
(a) State the definition of the derivative of the function
at the point
C& 5—B
±
B& ²
(b)
, find the derivative of the function
at the point
3.
Using the definition
C
&
B&
4
B
#
2.
(a) Let
. Find
and
.
4
2,
3
8,
3
1
,3
0—B±
&
³
0—B
±
0—B±
B
´
Bµ
B
¶
B·
&
±
²
2
33
3
li
m
m
lim
B
˜
B˜
B˜
´
¶
(b)
For what value(s) of will the following limit exist?
21
3
:
B ¶:B´
B´
B˜
3
2
3.
The temperature (C ) of a chemical reaction at time (sec.) can be modeled by the function
°
>
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(
6). (Note: This is
NOT .)
at
1 second.
X
&
>
±
69
1
6
8
>&
Estimate
.X
.>
4.
In this problem you are to construct a mathematical model from a table of data.
The table is shown
below, but only two data points are filled in.
>
C
2
??
1
5
????
5.
5??
464.
1????
The following are descriptions of some plots made from the complete table of data:
•
If we plot the points
(, ), we see a rising curve, which is concave up.
>C
•
If we plot the points
( ,
), we see a rising curve, which is concave down.
ln
•
If we plot the points (ln ,
), we see a line with positive slope.
ln
State what type of function would best model the relationship between and .
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 Spring '08
 Staff
 Calculus, Derivative

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