Math 1100
Name:
Exam 1A
key
25 September, 2013
UID:
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
25 September, 2013
Exam 1, Page 2 of 11
Math 1100
1. (6 points) Fill in the blanks:
(a) A derivative represents the instantaneous f
of a function at a point.
I
(b) A derivative is the slope of the
tion at a point.
(c) The derivative of a revenue function represents
to a func
1
a r,i
2. (8 points) Use the graph below to compute each of the following. Write DNE if it does
not exist.
.
-4
-
(a) f(-1)
t
t
(e) f(2)=
(b) lim
—1
=
(f) limx
2
=
(c) limx
—1
=
(g) limx
2
=
(d) limx——1=
IDNE
(h) limx—+2=
2
25 September, 2013
Exam 1, Page 3 of 11
Math 1100
3. (9 points) Determine whether each of the following graphs is continuous at x = 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)
k1O
Coih1UO1’5
jos viof
‘Ifr
(b)
C Of? ho”S
.
(c)
YW
coh.iv$.
IIVY)
I
.e.x’f.
Exam 1, Page 4 of 11
Math 1100
25 September, 2013
4. (9 points) Compute the following limits or state that they do not exist.
(a)
urn 4x
3
—
x—* 1
()3_7
1
i
2+ 1
2x
(b)
lirn
x-4
x +i
2
x 4
—
32 Q)
fr1of
e,isf.
(c)
lirn
x-—3 X
X--3
XI-
li
3
x-*-3
-
)c—-3
(x—3(xj.3)
X4- 3
—9
+3
(1)1
Math 1100
Exam 1, Page 5 of 11
25 September, 2013
5. (8 points) Use the definitioll of a derivative (not derivative rules) to compute the deriva
tive of
f(x)
3x 1
—
[3(yh)-tJ
-
[x-1)
-t
livll
Xf3Ji13Xl-i
h
-i
-
h-*P
Exam 1, Page 6 of 11
Math 1100
6. (16 points) Differentiate each function. Use any method you like.
(a)
1
y=3’
1
--+
I
3
—x
y
—
3(
9
+
3
9x
II
1X+
-x”
31
(b)
x+1
2
3x
—
(
2..
2
9x
-
Sicf3
2.
-
I
(continued on next page)
25 September, 2013
t
÷
1
U.
1-
-
1-
t
N
t:J
-
-h
(I
1’.)
+
+
II
(1%
-
‘1
I
II
I.
CD
CD
cr
CD
C)1
C
-
CD
tj
I’
Exam 1, Page 8 of 11
Math 1100
7. (9 points) Let y=\/+2x.
(a) Find
7.:i. X’-
L
-x
2
-“i
dx
zr
(b) Find
-3f7
2
X
1
c
jX
i
-LUi
(c) Find
-I
-3
3
25 September, 2013
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.
• 8
—x
(x+h)
lim
h—*O
h
j
—x
(x-
a
h
7
Zx
25 September, 2013
Exam 1, Page 10 of 11
Math 1100
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
=
=
x2
3
+ 4x
—
40
400
(a) Vs/hat is Carter’s profit on 20 servings of blue Jell-o?
(w).i- Lj(.)
.37
(b) What is Carter’s marginal profit function?
r
—3
LA)
zao
—
x
(c) What is Carter’s marginal profit at x
=
20?
P’(zo) z.zc
z0c
—3
Lj
37Q
(d) Use your answer to part (c) to estimate Carter’s profit from 30 servings of blue
Jell-o.
po) P(w)i- IOt(zt;)
74- lo(.7)
7f37
3
479
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 after f seconds
is given by
2 + 30t + 15
h(t) = 6t
(a) How high is Colonel O’Neill after 10 seconds?
h(io)
(D(to)t4 30(i)’
CJOfS
1
(b) What is Colonel O’Neill’s velocity after 10 seconds?
O
3
i,’(&) iz’‘H) LZt1)-3O
u-iSV
5
vq
(c) What is Colonel O’Neill’s acceleration after 10 seconds?
k”() 12.
V2
(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 von need to.
ck(-4
ve
c,
rh
sld
edIy
For
i’r€
hro’c h-
k-y.ns
ii’s
1
&VfLQ iviirc/
ol. dN;1J ‘iI (y
kfiIc
‘t.’I
e.1i
t-t
1-c
bras
sy51-evr’
lcX)
1l-.eq
A-sard.
(eS.
5
ec.i t’1o
1WY
h rv
Ieani
iviaify
fr Afl
reIihs ti
.,QCAd
Pk1jo
1v.e J.(f0
o