72 Answered Questions for the topic AP Calc

05/05/22

#### Optimization Help and explanation

A Norman window is shaped like a rectangle with a semicircle on top of it. A carpenter has 10m of wood trim and wishes to cover the sides of the rectangle and the upper part of the semicircle....
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05/05/22

#### Speedometer readings for a motorcycle at 12-seconds intervals are given in the table.

Speedometer readings for a motorcycle at 12-seconds intervals are given in the table.t (sec) 0 12 24 36 48 60v (ft/sec) 22 26 29 23 23 30(a) Estimate the distance, in feet, traveled by the...
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05/04/22

#### Estimate the area under the graph with midpoint?

Estimate the area under the graph of f(x) = 16 - x^2 from x=0 to x=4 using 4 approximating rectangles.I got the right sum = 34 and left sum = 50 but how do I estimate area with midpoints?

05/02/22

#### integral problem

The velocity function is v(t)=t2−3t+2 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [−3,6].displacement = ??distance...
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#### antiderivative velocity question

A particle moves on a straight line and has acceleration a(t)=18t+14.Its position at time t=0 is s(0)=6 and its velocity at time t=0 is v(0)=14.What is its position at time t=7?

05/02/22

#### antiderivatives question

Given that the graph of f(x) passes through the point (6,7) and that the slope of its tangent line at (x,f(x)) is 3x+2, what is f(2)?

05/02/22

#### Find two positive numbers whose product is 144 and whose sum is a minimum? Optimization Help

Find two positive numbers whose product is 144 and whose sum is a minimum.

05/02/22

#### Optimization Calculus Question

Find two numbers A and B (with A<= B) whose difference is 42 and whose product is minimaized.A = ???B = ???

04/22/22

#### Derivative integral Please Help

04/22/22

#### Integral Question

Consider the integral:21∫ x^3 dx3-Use Left Sum, Right Sum, Midvalue Sum, and Trapezoid Rule methods to approximate this integral with n = 3-Find the exact value of this integral

04/19/22

#### calculus integral question

Consider the integral:21∫ x^3 dx3-Use all three methods to approximate this integral with n = 3-Find the exact value of this integral

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

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