The average population of the city on [a, b]
The change in population of the city from time a to time b
The rate of population growth at time a
The population of the city at time b
B. The change in population of the city from time a to time b
The slope of the tangent line
The area under the curve
The concavity of the curve
The average rate of change
x^3 + C
x^2 + C
x^3/3 + C
3x + C
v42
v30
v29
v35
|a| × |b| × cos(?)
|a| × |b| × sin(?)
|a| + |b|
|a| - |b|
The average value of f(x) on [a, b]
The area between the curve y = f(x) and the x-axis on [a, b]
The derivative of f(x) at x = a
The slope of the tangent line to the curve y = f(x) at x = b
It depends on the specific curve C.
It is always zero.
It is equal to the area enclosed by C.
It is equal to the circumference of C.
Laplace transforms
Substitution
Separation of variables
Variation of parameters
f(x) = 1/x
g(x) = x^2 + 3x + 2
h(x) = |x - 2|
None of the above
A point in space
A scalar quantity
A quantity with magnitude and direction
A constant value
lim (x -> 0) (1/x)
lim (x -> 2) (x^2 - 4)/(x - 2)
lim (x -> 1) (x^2 - 1)/(x - 1)
lim (x -> 3) (1/x^2)
1
0
-1
Undefined
<1, 1>
<2, -1.5>
<4/5, -3/5>
<0, 0>
z = 2x - 3y + 5
z = 2x + 3y - 5
z = 2x - 3y - 5
z = 2x + 3y + 5
Separable
Linear
Exact
Homogeneous
e^(2x) + C
(1/2)e^(2x) + C
(1/2)e^(2x^2) + C
(1/4)e^(2x) + C
The average population of the city on [a, b]
The change in population of the city from time a to time b
The rate of population growth at time a
The population of the city at time b
12x^2 - 4x + 5
12x^2 - 4x - 5
12x^2 - 2x + 5
12x^2 - 2x - 5
0
1
7
-7
47
37
27
17
x = rcos(?), y = rsin(?)
x = r?, y = r?
x = cos(?), y = sin(?)
x = rsin(?), y = rcos(?)
2e^(2x)
e^(2x)
2e^(x)
e^(x)
The acceleration is positive.
The acceleration is negative.
The acceleration is zero.
Nothing about the acceleration can be determined.
0
1/4
1/3
1/2
arctan(x) + C
ln(x^2 + 1) + C
2arctan(x) + C
(1/2)ln(x^2 + 1) + C
4p
8p
16p
32p
Integral Test
Comparison Test
Alternating Series Test
Divergence Test
u = sin(x)
u = cos(x)
u = sec(x)
u = tan(x)
p square units
4 square units
2 square units
0 square units
(0, 0, 0)
(1, 1, 1)
(0, 0)
(1, 1)
y = x^3 + C
y = 3x + C
y = x^3/3 + C
y = 3x^3 + C