Spring 2013
February 11, 2012
Math 1310-001
Midterm #1
Midterm #1: Limits & Derivatives
Instructions: You may use a calculator to assist you with any arithmetic, a writing
utensil, and your 3x5 reference card that you have prepared. No other materials
are permitted. Please show all of your work to the level of detail that is specified
in the instructions for that particular problem. You MUST write your final answer
in the space provided to receive full credit. The point value of each problem is
specified in the problem statement. Most of the credit will be awarded for doing
the calculus correctly and showing the appropriate steps. A correct final answer
with no work supporting it will receive very few points!! You may turn in your
exam and leave when you have finished.
Recommendation: You do not need to work on these problems in order. I would
suggest first answering the ones you find the easiest. Then go back and work on
the harder ones at the end. Also, if you finish early I would suggest double
checking all of your work, just in case you made any very simple mistakes.
Name:
A ncuu
Spring 2013
February 11, 2012
Math 1310-001
Midterm #1
1.
Letf(x) be the function depicted in the figure below. Evaluate expressions forf(x).
Write your final answers in the boxes below. If the value does not exist, write “DNE” or
“Chuck Norris”. (10 points)
4—
—
y ‘f(x)
I
1
I {)j’qi
(a)
f(1)
(b)
+ f(x)
2
1im.,
(c)
2 f(x)
1im,
(d)
f(4)
=
,-
=
(e)
f
(x)
1im
f
4
=
—,
_\
=
L,IA’
UN £
=F
-
2
I
4
Math 1310-001
Midterm #1
Spring 2013
February 11, 2012
2.
Calculate the following limits. Show all of your work and write your answer in the box
below. If the limit does not exist write “DNE” or “Chuck Norris”. (15 points)
(a)
1
lim,
lv
—3x+2
2
x
=
—
-)(x-iJ
(
x41
(b)
0
l1m,
(x)
3
cos(x)sin
—
—
UJSyX)
I ‘y
Cs1J
(
liyV)
4.)
)LJ
(1)(fl’(()
(c)
1
11m,
X
=
-
I
—
-
( z)
)
1 )
iVi
+
—
L
(+)
-t(
—
i i
z
X-I)( f2)
I
,
fril
—
—
Spring 2013
February 11, 2012
Math 1310-001
Midterm #i
3.
What value of a will make f(x) a continuous function? Show all of your work and write
your final answer in the box below. (10 points)
—6x-i-9
2
‘x
f(x)
=
a
if
x*3
if
x=3
jC
O1
(f
j
b)(x-
(
0
QLof
0
Spring 2013
February 11, 2012
Math 1310-001
Midterm #1
Let f(x) = x
4.
3 + 5. Use the limit definition of the derivative to find f’(x). Show all of
your final answer in the box below. (10 points)
and
write
work
your
f’(x)
2
=
47)
/4
±
ii
(;
h
. 3k ÷
2
x
0
41
Spring 2013
February 11, 2012
Math 1310-001
Midterm #1
A ball is dropped from the roof of a 5Gm building. The function describing its height
5.
. Answer the following questions about
2
above the ground at a given time is h(t) = 50 4.9t
the ball. You may use the rules of differentiation rather than the limit definition of derivatives
on this problem. Show all of your work and write your final answer in the box below. (10
—
points)
What is the function, u(t), that describes the balls instantaneous velocity at a given
time?
(a)
v(t)
=
\ii+)
What is the value oft at the moment the ball is 10 meters above the ground?
(b)
t
=
9•
j2-
Lid
Lyl:
itth iO
2
L/
_Lj,Q-f’
(0
-140
What is the instantaneous velocity of the ball at the moment it is 40 meters above the
ground?
(c)
Velocity=
()
çç
.
..(qiL
5
‘V
a’d
lz 1
,fl
L
3
S
41) -f 41
-
- 4O
2
5
1
O- q.q
_L(,7t —L)
::::
J
2
I’)
Lj4
1
‘ii’,
1)3
e.
Math 1310-001
Midterm #1
Spring 2013
February 11, 2012
Use the rules of differentiation to find the derivatives of the following functions.
6.
Assume that a and b are constants. Show all of your work and write your final answer in the
box below. (10 points)
(a)
—(x +5x
2 _aex)
=
(x?i
(b)
Jx
2
1
bL
2 —3x+2
1x
bx
)=
h.x
(hc
I2
_2)
-
dY
(c)
(1+V)=
2
21)
=
::
-1
2
I
—1
K
‘I
4
1’
I
-
I
K
.1
-K
C-
a
;.
,
4.
-
‘-r
.4
-K
a,,
c•
‘a-
4