25 September, 2013
Exam lB
Math 1100
UID:
Name:
Instructions:
• Answer each question in the space provided.
• No calculators are allowed.
Question
Points
1
6
2
8
3
9
4
9
5
8
6
16
7
9
8
10
9
16
10
9
Total:
100
Score
Math 1100
25 September, 2013
Exam 1, Page 2 of 11
1. (6 points) Fill in the blanks:
(a) A derivative is the slope of the
tion at a point.
Likf
fve’i4
(b) A derivative represents the instantaneous
of a function at a point.
Ck
(c) The derivative of a revenue function represents
to a func
o ck
5i
r
I
2. (8 points) Use the graph below to compute each of the following. Write DNE if it does
not exist.
(a)
f (-1)
2
=
(b) limx
(e) f(2)
—1
(f) limx
(c) limx
—+
—1
(d) limx
—
—1
=
=
Q
I
=
2
=
=
(g) limx
—+
2
(h) 1im
—
2
=
—1
I
-
Math 1100
25 September, 2013
Exam 1, Page 3 of 11
3. (9 points) Determine whether each of the following graphs is continuous at r = 1. If
not, explain why not. Your explanation should reference the definition of continuity
and/or the three conditions required. (Write your answer to the right of each graph.)
(a)
(b)
PC,’-
Coil hvivwS;
(c)
coil
(V
i-tx)
dc)
ex
Math 1100
Exam 1, Page 4 of 11
25 September, 2013
4. (9 points) Complite the following limits or state that they do not exist.
(a)
lim 2x
3 + 2T + 4
x—+ 1
4-Lx3
Z A
(b)
lim
x-*3
33
2+9
x
3
—
0
ex,SI
(c)
lim
jIkt
X-4-2
(XfZ)(.i)
X—-2
(x)
c-z
_L1
4
x+2
Exam 1, Page 5 of 11
Math 1100
5. (8 points) Use the definition of a derivative
tive of
f(x)
, LLixh)zJ
—
(not
=
1141
-
l1-)
-
derivative rnles) to compute the deriva
4x + 2
L’L1x.,zJ
1,
4Lk1Z_Cly-Z
25 September. 2013
Exam 1, Page 6 of 11
Math 1100
6. (16 points) Differentiate each function. Use any method you like.
(a)
—
7
x
-
3
7x’*Zx
_7
ix
+
Z
-
(b)
g(x)
-
(SXL)
--1
:x
xg
9
1
(continued on next page)
x+1
=
32
25 September, 2013
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t
t
9
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ii
+
+
II
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II
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CD
CD
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I.
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+
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II
Math 1100
Exam 1, Page 9 of 11
25 September, 2013
8. (10 points) Evaluate the following limit. Show your work. Your answer will be a function
of x and should be simplified.
• 6
—x
(+1i)
hm
Ii
h
(h)&_c
Math 1100
25 September, 2013
Exam 1, Page 10 of 11
9. (16 points) Samantha Carter wants to open a restaurant that serves blue Jell-o. She
estimates that her profit in dollars from selling x servings of blue Jell-o will be
P(x)
For reference: 202
=
=
52
+4x
—
40
400
(a) What is Carter’s profit on 20 servings of blue Jell-o?
P(z
(w)’ (zo)-o
-Sf-
O-Ljt,
$35(b) What is Carter’s marginal profit function?
)C)
-
X
20
4-9
(c) What is Carter’s marginal profit at x
‘(2O
j-- (u)
=
20?
1L1
3.SO
(d) Use your answer to part (c) to estimate Carter’s profit from 30 servings of blue
Jell-o.
P(3o) PftC)i- io.P’(z)
.
jc-
$7Q
lOb(3.5)
25 September, 2013
Exam 1, Page 11 of 11
Math 1100
10. (9 points) Colonel O’Neill is flying an X-301 aircraft. Its height in meters aft.er t seconds
is given by
2 + 20t + 15
h(t) = 8t
(a) How high is Colonel O’Neill aft.er 10 seconds?
(1o- uCio)
&lOO
i-
is
i-1
(b) ‘vVhat is Colonel O’Neill’s velocity after 10 seconds?
e 1(é 4-ZC
j
(
1
k(1o) l1toF it)
L)
vk1/
(c) What is Colonel O’Neill’s acceleration after 10 seconds?
“‘e) 1(
z
(d) (0 points) What do you think would happen if Colonel O’Neill and Samantha
Carter teamed up to fight aliens? You may answer in words or pictures. Use
the back of this sheet if you need to.
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