Math 1100-3
Babenko V.
September 22, 2015
Test 1
Name:
UID#:
This is a closed book Test. No books, laptops, or messaging are permitted. NO calculators
are allowed. You have 15 problems, they are equal in weight. The entire exam is worth 15
points. For full credits show all work! Box your answer so it is easy to locate. You have
60 minutes.
GOOD LUCK!!!
1
1. Use properties of limits and algebraj methods to find the limit, if it exists.
Jim
X—*-1/2
-
2
2+9
8x
8x
—
4-2
(.1
) -t
-
—
2. Use properties of limits and algebraj methods to find the limit, if it exists.
—
Jim
L
2..
-
2
3. Determine whether the function is continuous or discontinuous at the given x-value.
Examine the three conditions in the definition of continuity.
—25
x—5
) f
)
(- s)
x=—5
s)
x-S
J cA-s
4
-e
Q
z)
x-s
4. Determine whether the function is continuous or discontinuous at xr=1. Examine the
three conditions in the definition of continuity.
f(x)
=
fx2+8
6x2 3
—
if
if
x<1
x> 1
%)
(‘ -
\\
_S
—
I
-
L— \
3
5. If
urn f(x)
=
urn g(x)
9 and
a) lim[f(x) + g(x)j
=
—5 find the following.
—
x—*3
tC—s
—
b)i{f(x)-g(x)]
—
—
c) 1[f(x) g(x)]
-f4
1
d)1im
g
—
—
x—>3 Y
4
—
U
-
N
—
I
ii
5’—,
+
N
1
?<
--
‘I
4-
or
11
I
+
‘O
2
?
+
-t
2<
c’o
(N
x
g
II
-
1
+
pa
6. Let f(x)
=
2
3x
—
2x.
a) Use the definition of derivative to find the derivative
))
Lt32L
_-L---
c) -
—
a
÷C
k)a_(x÷L
=
L
b) Find the instantaneous rate of change of f(x) at x
=
—2
1I-2 —I
(-2) (_2—2
c) Find the slope of the tangent to the graph of y
=
f(x) at x
7. Find the derivative of the function
a)y=100
b)f(x)=5x
9
c)y=t
d) s(t)
=
2
2
t’/
—
5
e)g(x)=7x
+
3
—
2
x+11
6x
4x
-)
1Z
5
=
—2
2
10. If y
=
Vx2
—
1, find
using chain rule.
a-u
a-u
11. If y
=
2
(x
—
, find
6
4x)
-
1
V
—
---LL
2
using power rule.
7
K
12. Find f’(x) if f(x)
1
=
(x +3)
DO NOT SIMPLIFy
3
_4
13. If y
find y’. DO NOT SIMPLIFy
a
(5)
q
()
8
14. Find the first four derivatives of f(x)
=
3+2
5x
4x + 9x + 7.
a
Ti
lI(%)
-
LII
L)
bc
=0.
15. The revenue from the sale of x units of a product is represented by the following
formula.
R = 21(2x + 1)—’ + x 5 dollars.
Find the marginal revenue when 10 units are sold.
—
—2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
-2L2
(210 4L
-+‘
21
21
Total
L-Hi
9
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/ 150
/15
a