4 Given that
and
Evaluate the limit:
a.
b.
c.
d.
15
17
14
2
10
Find the slope of the tangent line to the parabola
135).
a.
29
b. 21
c. 34
at the point (9,
d. 24
15
Find the limit.
a.
b.
c.
d
16
Find the limit if it exists.
a.
b.
3
c. 2
d. 6
e DNE
17
Find the limit if it exists.
a.
b.
c.
d.
the limit does not exist
18
Find the limit if it exists.
a.
b. - 5
c.
d.
e. 0
19
Use the graph of the function f to find
, if the limit exists.
a.
b.
c.
d.
and
20
Refer to the graph of the function
a.
2
b. 0
lim
f (x)
x → 0−
c.
4
d. DNE
21
Find the one-sided limit, if it exists.
a.
b.
c.
d.
e.
The limit does not exist
24 Determine all values of x at which the function is discontinuous.
a.
b.
c.
d.
22 Continuity at a Point. A function f is continuous at the point
conditions are satisfied.
1.
is defined.
2.
if the following
exists.
3.
.
Determine the values of x, if any, at which the function is discontinuous. At each point
of discontinuity, state the condition(s) for continuity that are violated.
a.
b.
c.
d.
e.
Continuous everywhere
25 Find the derivative of the function by using the rules of differentiation.
a.
b.
c.
d.
26
Let
Find
a.
b.
c.
d.
27
Find the derivative of the function.
a.
b.
c.
d.
28
Find the derivative of the function.
a.
b.
c.
d.
31
Find the derivative of the function.
a.
b.
c.
d.
d.
33
Find the derivative of the function.
a.
b.
c.
d.
34
Find the derivative of the function.
a.
b.
c.
d.
42 Differentiate.
a.
g(x) = 2 sec x + tan x
b.
c.
d.
43
Differentiate.
a.
b.
c.
d.
54 Find g’(x) by evaluating the integral using Part 2 of the Fundamental Theorem and then
differentiating.
a.
b.
c.
55
Evaluate the integral.
a.
126
b. -18
c. -90
d.
-486
56
Evaluate the integral.
a.
58
1
b.
2
c. -1
Evaluate the integral by making the given substitution:
a.
b.
c.
d.
d. 0
∫x
2
x 3 + 5 dx
61
Evaluate the indefinite integral:
a.
b.
c.
d.
76
Find the absolute minimum values of
on the interval [0,
5].
a.
64
b.
-126
c.
-128
d.
4
79 Verify that the function satisfies the hypotheses of The Mean Value Theorem on the
given interval. Then find all numbers c that satisfy the conclusion of The Mean Value
Theorem.
a.
b.
c.
d.
80 Find the intervals on which the following function f is increasing:
a.
b.
c.
d.
(-6, 6)
e.
81 Find the inflection points of the following function:
f ( x ) = -2 x + 2 - 2 sin x
a.
b.
c.
d.
82 How many points of inflection are on the graph of the function:
a.
3
b.
2
c.
4
d.
1
83 Find two positive numbers whose product is 144 and whose sum is a minimum.
a.
4, 36
b.
2, 72
c.
12, 12
84 Consider the following problem: A farmer with 850 ft of fencing wants to enclose a
rectangular area and then divide it into four pens with fencing parallel to one side of the
rectangle. What is the largest possible total area of the four pens?
a.
18062.5
b.
18051.5
c.
d.
18061.5
18085.5
94
Evaluate the indefinite integral:
a.
b.
c.
d.
100
Find
a.
by implicit differentiation.
b.
c.
d.
101
Find
a.
b.
c.
d.
by implicit differentiation.
107 The base of a 80-ft ladder leaning against a wall begins to slide away from the wall.
At the instant of time when the base is 64 ft from the wall, the base is moving at the
rate of 9 ft/sec. How fast is the top of the ladder sliding down the wall at that instant of
time?
a.
7.8 ft/sec
b.
11.7 ft/sec
c.
13.6 ft/sec
d.
12 ft/sec
Answer from math1920 key:
1 Find the volume of the solid obtained by rotating about the x-axis the region under the
curve
from x = 4 to x = 5.
a.
b.
c.
11 Find the derivative of the function.
a.
b.
c.
d.
12 Find the derivative of the function.
a.
b.
c.
d.
10
Find the derivative of the function.
a.
b.
c.
d.
13 Find the derivative of the function.
a.
b.
c.
d.
14 Find the derivative of the function.
a.
b.
c.
d.
15 Find the derivative of the function.
a.
b.
c.
d.
16 Use the arc length formula to find the length of the curve
Check your answer by noting that the curve is a line segment and calculating its length
by the distance formula.
a.
b.
c.
d.
17 Set up, but do not evaluate, an integral for the area of the surface obtained by rotating
the curve about the given axis.
a.
b.
c.
d.
33 Find the volume of the solid obtained by rotating about the x-axis the region under the
curve
from x = 7 to x = 9.
a.
b.
c.
34 Find the volume of the solid obtained by rotating the region in the first quadrant
and
about the y-axis.
bounded by
a.
b.
c.
37
Differentiate the function.
a.
b.
c.
d.
39
Evaluate the integral.
a.
b.
c.
d.
40
41
42
39
45 Use logarithmic differentiation to find the derivative of the function.
a.
b.
c.
47 Use logarithmic differentiation to find the derivative of the function.
a.
b.
c.
10
9
Find the indefinite integral.
Hint:
a.
b.
c.
d.
11
2
Find the indefinite integral.
a.
b.
c.
d.
Use the graph below to answer the following questions.
1. What type of discontinuity exists at x= 1.5?
a. jump
b. infinite
c. removable
d. the function is continuous at 1.5
2. Find the one sided limit:
a. 0
b.
2
c. - ∞
d.
∞
Use the graph above to answer the questions below.
____1.
f ′( x ) = 0
a. infection point
____2. f ′′ < 0
b. critical points
____3. f ′′ = 0
c. curve is increasing
____4. f ′( x ) > 0
d. local minimum
____5. Inflection point
e. curve is concaved up
____6. [ 0, 3 ]
f. curve is concaved down
____7.
g. curve is decreasing
(2, -3)