800 Answered Questions for the topic AP Calculus

#### A projectile moves with a position vector so that its horizontal component is x(t) = 140t and its vertical component is y(t) = -5t2. Which of the following is the vertical component of the...

A projectile moves with a position vector so that its horizontal component is x(t) = 140t and its vertical component is y(t) = -5t2. Which of the following is the vertical component of the...
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#### Find the slope of the tangent line to the graph of r = 1 + cos θ, at theta equals pi over 6

Find the slope of the tangent line to the graph of r = 1 + cos θ, at
A
-1
B
0
C
1
D
Undefined

#### Which of the following is the Cartesian equation for the polar equation r = -6 sin (θ)?

Which of the following is the Cartesian equation for the polar equation r = -6 sin (θ)?
A
x2 + y2 = 9
B
x2 + (y - 3)2 = 36
C
x2 + (y + 3)2 = 9
D
(x - 1)2 + y2 = 9

#### Find the slope dy dx of the polar curve r = 1 + 2 sin θ at θ = pi over 2

Find the slope of the polar curve r = 1 + 2 sin θ at θ =
A
Undefined
B
1
C
-1
D
0

#### Find d 2 y over d x squared for the curve given by x = 1 - t2 and y = 10t + 1

Find for the curve given by x = 1 - t2 and y = 10t + 1
A
B
0
C
D
None of these

#### Find dy dx for the parametric equations x equals one half t squared and y = t2 + t

Find for the parametric equations and y = t2 + t
A
B
C
2
D

#### A particle moves in the x-y plane for t > 0 so that x(t) = t3 - 4t and y(t) = et. At time t = 1, the particle is moving

A particle moves in the x-y plane for t > 0 so that x(t) = t3 - 4t and y(t) = et. At time t = 1, the particle is moving
A
to the left and up
B
to the right and up
C
to the left and...
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Ap Calculus

1d

#### Cross-Section Volume

Find the volume of the solid formed by a base with the region bounded by the graphs of y = x^1/2, y = 0 and x = 2, and cross-sections that are squares perpendicular to the x-axis.

Ap Calculus Calculus

3d

#### Mean value free response?

The continuous function f is defined on the closed interval [-5,5]. The graph of f consists of a parabola and two line segments. Let g be a function such that g'(x)=f(x). There is no value of x in...
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#### Determine the area of the inner loop of the polar curve r = 1 − 2 sin (θ)

Determine the area of the inner loop of the polar curve r = 1 − 2 sin (θ)Type your answer in the space below and give 3 decimal places. If your answer is less than 1, place a leading "0" before the...
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#### Find the area of the region that is inside the graph of r = 5 sin θ and outside of the graph of r = 2 + sin θ

Find the area of the region that is inside the graph of r = 5 sin θ and outside of the graph of r = 2 + sin θ
A
10.109
B
3.323
C
6.646
D
20.219

#### Find the area enclosed by the cardioid r = 6 + 6 cos θ

Find the area enclosed by the cardioid r = 6 + 6 cos θ
A
9π
B
54π
C
27π
D
108π

#### Find the area of one petal of the polar curve r = 5sin 2θ

Find the area of one petal of the polar curve r = 5sin 2θ
A
B
C
D
π

#### Find the point(s) of intersection for the polar curves with equations r = 6 cos θ and r = 4 − 2 cos θ

Find the point(s) of intersection for the polar curves with equations r = 6 cos θ and r = 4 − 2 cos θ
A
B
C
D
0, π

#### Find the arc length of the curve from t = 0 to t = 4 whose derivatives in parametric form are dx dt equals the sine of t and dy dt equals the natural log of the quantity t squared plus 2 .

Find the arc length of the curve from t = 0 to t = 4 whose derivatives in parametric form are and .Type your answer in the space below and give 2 decimal places. If your answer is less than 1,...
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#### What is the length of the curve x = y3/2 from y = 0 to y = 4?

What is the length of the curve x = y3/2 from y = 0 to y = 4?
A
None of the choices below
B
C
D

#### What is the length of the path along the graph of y equals the square root of the quantity 16 minus x squared between x = 2 and x = 4?

What is the length of the path along the graph of between x = 2 and x = 4?
A
B
C
D

#### What is the length of the curve with parametric equations x = 1 - 2cos(t), y = 2 - 2sin(t) from t = 0 to t = π ?

What is the length of the curve with parametric equations x = 1 - 2cos(t), y = 2 - 2sin(t) from t = 0 to t = π?
A
8
B
4
C
8π
D
2π

#### A point has a position vector given by r of t equals the vector with components t, 4 , for all time t ≥ 0 seconds. Find the speed of the object at t = 3 seconds.

A point has a position vector given by , for all time t ≥ 0 seconds. Find the speed of the object at t = 3 seconds
A
B
1
C
0
D

#### Find the magnitude of a particle's acceleration vector at t = 0 for a particle moving with position vector r of t equals components the cosine of t, t cubed

Find the magnitude of a particle's acceleration vector at t = 0 for a particle moving with position vector
A
1
B
0
C
2
D
3

#### What is the velocity vector for a moving particle with a position vector r of t equals the components 2 over t, the natural log of t ?

What is the velocity vector for a moving particle with a position vector ?
A
B
C
D

#### What is the direction of the vector r of t equals the vector with components 1, 1 ?

What is the direction of the vector ?
A
1
B
C
D

Ap Calculus

6d

#### b. How many people are in the museum after 10 hours?

this is part b from my last questionhere is the full question: The graph below shows the rate of change for the number of people in a museum 𝑡 hours after it opens.a. How many people are in the...
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#### The components of a position vector of a particle moving in the plane are components 2 times t squared, cosine of t . What is the distance traveled by the particle from t = 0 to t = π?

The components of a position vector of a particle moving in the plane are . What is the distance traveled by the particle from t = 0 to t = π?Type your answer in the space below and give 3...
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#### A point has a position vector given by r of t equals the vector with components t, 4 , for all time t ≥ 0 seconds. Find the speed of the object at t = 3 seconds

A point has a position vector given by , for all time t ≥ 0 seconds. Find the speed of the object at t = 3 seconds
A
B
1
C
0
D

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