1,125 Answered Questions for the topic AP Calculus

Ap Calculus

01/04/22

A particle moves along the x-axis so that its position at anytime t>= 0 is given by the function x(t)=t^3-12t+2 where x is measured in feet and t is measured in seconds.

A Find the displacement during the first 3 seconds. In which direction did the particle move? B At what value(s) of t does the particle change direction? Explain your reasoning. C When does the... more
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Ap Calculus Math

12/18/21

Implicit Derivative at a Point

If xy + 3 - 4y = 0 then find the equation of all tangent lines to the curve when x = 5
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Ap Calculus Math

12/17/21

Implicit Derivative at a Point

If 1 + 3y = xy then find the equations of all tangent lines to the curve when x=2
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Ap Calculus

12/10/21

How do I sign up for instant tutoring?
AP Calculus AB homework assignment
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Ap Calculus Math Calculus Physics

12/06/21

A 7.6 −kg box having an initial speed of 4.5 m/s slides along a rough table and comes to rest.
A 7.6 −kg−kg box having an initial speed of 4.5 m/sm/s slides along a rough table and comes to rest.Estimate the total change in entropy of the universe. Assume all objects are at room... more
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Ap Calculus Math

12/01/21

Determine Increasing/Decreasing and Concavity
Given the function f(x)= 3x^4−12x^3, determine all intervals on which f is both decreasing and concave up.
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Ap Calculus

11/23/21

calculus related rates
A man 6-ft tall walks at a rate of 5 ft/sec. away from a lamppost that is 22-ft high. At what rate isthe length of his shadow changing when he is 60 feet away from the lamppost?
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Ap Calculus

11/23/21

calculus related rates
Sand is falling from a conveyor at a rate of 28 ft3/min onto the top of a conical pile. The height ofthe pile is always 1⁄2 of the base diameter. How fast is the height changing when the pile is 12... more
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Ap Calculus

11/23/21

Calculus related rates
A container is the shape of an inverted right circular cone has a radius of 5 inches at the top anda height of 7 inches. At the instant when the water in the container is 3 inches deep, the... more
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Ap Calculus Math Calculus

11/17/21

Let F(x) = ∫ 12x (sqrt (t^2 + t)) dt Find the domain of F in terms of x.
Let F(x) = ∫12x (sqrt (t^2 + t)) dtFind the domain of F in terms of x.
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Ap Calculus

11/16/21

Calculus derivatives and tangent line
Consider the curve x^2y + y^2x = 6 A) Find dy/dx in terms of x and y B) Write the equation for the tangent lien where x =2 and y=1C) Find the coordinates of the point (x,y) where the curve has a... more
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11/13/21

Please help with math
1) Find f. f '''(x) = cos(x),    f(0) = 4,    f '(0) = 8,    f''(0) = 72) A particle is moving with the given data. Find the position of the particle, s(t).a(t) = t^2 − 7t + 4, s(0) = 0, s(1) =... more
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Ap Calculus Math Calculus

10/31/21

The rate at which tickets were sold for [0, 9] is modeled by… r(t)=550te-t/2 tickets per hour. Based on the model, how many tickets were sold by 9 P.M. (t=3) to the nearest whole number?
Concert tickets went on sale at noon (t= 0) and were sold out within 9 hours. The number of people waiting in line to purchase tickets at time t is modeled by a twice-differentiable function L... more
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Ap Calculus Math Calculus

10/31/21

Water is draining out of a tank. If the rate of the leak is modeled by Q(t)=16.78sin(0.15x-1.25)+14.6, at what time is the rate of the leak increasing the fastest?
Water is draining out of a tank.If the rate of the leak is modeled by Q(t)=16.78sin(0.15x-1.25)+14.6, at what time is the rate of the leakincreasing the fastest?Use your calculus knowledge and show... more
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Ap Calculus

10/24/21

ap Calculus please explain

The second derivative of the function f is given by f''(x)=x(x-a)(x-b)^2. The graph of f'' is shown above. For what values of x does the graph of f have a point of inflection?how do I upload the... more
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Ap Calculus Math Calculus Physics

10/18/21

Help needed with math question
1.Given s = t4 − 4t3 − 20t2 + 15t, where t ≥ 0, at what time is the acceleration 0?2.Given: A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in... more
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Ap Calculus Math Calculus

10/17/21

Solve the following integral problem and show steps:
Solve and show clear steps:∫ (e(2t+4)^2 * (t+2)) dt
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Ap Calculus

09/24/21

Find the limit with work so i could understand

lim_x->4(x^(2)-6x+8))x2-x-12 = Limx->2 x3 + 8x+2 = Lim x-> 33x2 -8x-3 x- 3 =
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Ap Calculus Calculus Limits Derivative

09/20/21

Trigonometric Derivative as a Difference Quotient
I understand that the 2x might be treated as h. However, I don't know how to deal with cotangent.Limit (as h -> 0) of [8 * cot3(2x + pi/3) - 8 * cot3(pi/3)]/h
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Ap Calculus Calculus Limits Derivative

09/20/21

Trigonometric Derivative as a Difference Quotient
I understand that the 2x might be treated as h. However, I don't know how to deal with cotangent.Limit (as h -> 0) of [8 * cot3(2x + pi/3) - 8 * cot3(pi/3)]/h
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Ap Calculus Calculus Derivative

09/20/21

Calculus Problem Question, Elastic band
An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically.The equation of motion is s(t) =... more
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Ap Calculus

05/24/21

AP Calculus AB MCQ
A particle moves along the x-axis so that at any time t ≥ 0, its velocity is given by v(t) = cos(2 - t^2). The position of the particle is 3 at time t = 0. What is the position of the particle when... more
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05/22/21

For the function shown below, find each of the following limits. (If an answer does not exist, enter DNE.)
f(x) = 7x, x ≤ 0 x2 + 9, x > 0'(a) lim f(x) = _____ x→0−(b) lim f(x) = _____ x→0+(c) lim f(x) = _____ x→0
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Ap Calculus Math Calculus Mathematics

05/20/21

Help with Calculus!
A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of... more
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Ap Calculus

05/20/21

A cannon fires a cannonball (from ground level) with an inital velocity of 300 feet per sec with an angle of inclination of 50°.
A cannon fires a cannonball (from ground level) with an inital velocity of 300 feet per sec with an angle of inclination of 50°.1. Find the parametric equations that describe the position of the... more
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