60 Answered Questions for the topic AP Calc

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

#### 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

#### 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

#### 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

#### 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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#### . A spaceship weighs 50 tons on the launch pad. As it ascends, it burns fuel so that it weighs 20 tons by the time it reaches an altitude of 70 miles.

How much work is done in lifting the spaceship to an altitude of 70 miles? a. 2450 mi-tons b. 2100 mi-tons c. 3500 mi-tons d. none of these

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