61 Answered Questions for the topic AP Calc

11/24/20

#### FrQ AP CALCULUS

A particle moves along a straight line. For 0 ≤ t ≤ 5, the position of the particle is given by s(t) = 3t + 4t2 - t3.a) What is the average velocity of the particle over the interval 0 ≤ t ≤ 4? b)...
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01/06/18

#### How do I solve this? (question too long)

The top of a 15-foot-long ladder rests against a vertical wall with the bottom of the ladder on level ground, as shown above (it's just a ladder leaning against a wall). The ladder is sliding down...
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10/18/17

#### Find the derivative using limit process. -3x+2. Find the slope when x=4

i know how to do the derivative part but I don't know what to do with the x=4

02/07/16

#### Calculus integration question

The rate of depreciation dV / dt of a machine is inversely proportional to the square of t + 1, where V is the value of the machine t years after it was purchased. The initial value of the machine...
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02/07/16

#### Use the differential equation and the given point to find the equation of the function. (give your answer correct to three decimal points)

The given point is (-1,3).
The differential is dy/dx= -30/(4x+1)3

02/07/16

#### Find F as a function of x

The question states:
F(x)= int_1^x(t3+7t-6)dt
( F(x) is the integral of (t3+7t-6)dt from x to 1)

02/07/16

#### Determine the area under the given curve

The equation is 1/(x8). The limits are x=1 and x=2. I put this into my graphing calculator and it gave me an answer of 0.142 but the answer is not right apparently. Please help!

#### True or false. If true, why? If false, what is a counter example, and can you explain why it contradicts? Please

If f and g are differentiable and f(x)≤ g(x) on [a,b], then f'(x)≤g'(x) on [a,b]

#### True or false. If true, why? If false, what is a counter example, and can you explain why it contradicts? Please

If f and g continuous function on [a,b] then (upper: b, lower a)∫f(x)g(x)dx=[(upper: b, lower a)∫f(x)dx]*[(upper: b, lower a)∫g(x)dx].

#### True or false. If true, why? If false, what is a counter example, and can you explain why it contradicts? Please

If F(x)= (upper: x, lower: 0) ∫√(t3+1)dt then F'(2)=3

#### find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis.

finding the volume of the solid

#### the region bounded by y=0 and y=kx-x^2 is revolved around the y-axis to form a solid whose volume is 10.

what are the exact possible values of k? Hint: use cylindrical shells

#### exact solution to differetial equation

dy/dy+xy=x , y(0)=1/2

#### exact solution to differential equation

y'= (3-x)/xy , x>0, y(1)=2

#### the area of the region bounded by y=x^2 and y=x is________.

a. 1/6
b. 1/3
c. 1/2
d. 5/6
e. 1

#### Consider the region, R, bounded by the x-axis, the y-axis, and the graphs of the equations y=1/(x^2+1) and y=lnx

Find the area of the region R. a. 5.497 b. 1.483 c. 0.879 d. 0.013

08/22/15

#### Suppose we have a rod that is 6 meters long, with density function p(x)=2x+3. What is the center of the mass of the rod?

¯x= 11/3
¯x= 8/3
¯x= 14/3
¯x= 4/3
none of these

08/22/15

#### probability and integrals

Suppose that f(x) is the probability density function describing the distribution for the number of minutes it takes to solve a puzzle. Which of the following represents the probability that you...
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#### Given the cost function C(x), the marginal cost is given by which of the following?

a. ∫C(x)dx
b. ∫xC(x)dx
c. C'(x)
d. ( C'(x) )/x
e. none of these

#### center of mass

Particles A and B are located on the x-axis. The masses and positions of the particles are: mA = 12 grams xA = 2 mB= 8 grams xB = 10 What...
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#### stretching a spring

Suppose that a force of 20N stretches a spring 0.4 m beyond its natural length. How far will a 40N force stretch the spring? a. 1.0 b. 0.4 c. 0.2 d. 0.8

08/22/15

#### differential equation

Suppose that 120 deer are placed in a protected region. If the region can support a maximum deer population of 500, then the bounded growth model for the deer population gives us which differential...
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#### center mass of a rod

If you have a rod of length 5 with density p(x)=2+(x/5). What is the center of mass of the rod? a. ¯x=2.5 b. ¯x=2.667 c. ¯x=3.333 d. ¯x=2.165

#### work due to gravity

The force pulling an object to earth is where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the distance between the object and the center of...
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