Midterm 1
Calculus I (12010-007)
Answer the questions in the spaces provided. Show your work.
Name:
ID:U
Question:
1
2
3
4
5
6
Total
Points:
15
15
10
20
30
10
100
Score:
1. Find the following limits.
(a) 5 points lim
x*i
(b) 5 points
2 + 4r 5
x
8x + 7
urn
n—*+
—
c-u
-
—
3 + 4n
8n
2 +5
k
0
—.
t
ci)
c cf
-r
cD
cJD
.
—
riD
C
C
C-)
bID
C
ci)
C
C
C.)
CI
+
cD
cD
-
LCD
.
-e
t i/
2
N
0
ft
ci)
biD
2x
1
(b)
10 points
f(x)
=
—
2x2
if
<
—1
2
atx=—1
—i
if —1<x<0
2x2_3
ifx>0
Jv- N)
(_7
-
L
c\,\
(-fç,’3
,)-::
j’
‘k_)
c:
—\
V
S Qt&
h
.-
(2sinx
if x
0
3. 10 points Verify that the function f(x) =
is discontinuous at x =
x
0
atx=O
0. Is it a removable discontinuity? If so, remove the discontinuity and redefine the
function so that it is continuous.
‘—?
w)
()D
)
,
Page 3
4.
(a) 5 points Find the equation of the tangent line to the curve y
point (1,1/5).
=
2
x+4
at the
—
‘)\
)
2
‘
I
—
4
-
(b) 5 points Find all points on the graph of
horizontal.
Page 4
=
—
2
where the tangent line is
(c)
10 points A particle travels as a function of time according to the formula
s
. where s is in meters and t is in seconds. Find the velocity
3
100 + lOt + O.01t
and acceleration of the particle at t = 2.
S: O-kOQk
5. Find
dx
¶ O:l
for the following functions.
—
(a)
10 points y
=
x- + x
—
i
1-
/
(b)
10
.
Islnx
points
y
=
\cos
(
\4
2x
‘
Y
Page 5
a
H-I
fl
>
I
r
5
(1
flN
:
-
çc
C
II
c-km
CI