1,131 Answered Questions for the topic AP Calculus

Ap Calculus Calculus

04/27/21

Steps Needed To Solve This Problem?
Let y= f(x) be the particular solution to the differential equation dy/dx= y2 with the initial condition f(1)= 1. Which of the following gives an expression for f(x) and the domain for which the... more
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Ap Calculus Calculus

04/27/21

General and particular solutions help?
Let y= f(x) be the particular solution to the differential equation dy/dx= 1/(2y+1) with the initial condition y(0)= 0. Which of the following gives an expression for f(x) and the domain for which... more
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04/23/21

Find the range of the function f of x equals the integral from negative 4 to x of the square root of the quantity 16 minus t squared
 Find the range of the function  .A)[-4,4]B)[-4,0]C)[0,4pi]D)[0,8pi]My answer is C
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04/23/21

Pumping stations deliver gasoline
Pumping stations deliver gasoline at the rate modeled by the function D, given by  with t measure in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations deliver... more
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04/22/21

The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.
The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.Using a right Riemann sum with 5 subintervals estimate the total... more
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04/22/21

Which of the following functions grows the fastest as x goes to infinity
a)2xb)ln(x)c)sin(x)d)x20my answer is d
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Ap Calculus

04/22/21

Find the area of the region enclosed

Y=-9x^2-48x-39 and y=-4^2-3x+1 between x=-2 and x=3
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04/21/21

The graph of f ′(x) is continuous and increasing with an x-intercept at x = 0. Which of the following statements is false?
a)The graph of f is always concave up.b)The graph of f has an inflection point at x = 0.c)The graph of f has a relative minimum at x = 0.d)The graph of the second derivative is always positive.
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04/21/21

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 4 of x squared, dx
Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for 
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04/20/21

Given f(x) > 0 with f ′(x) < 0, and f ″(x) > 0
Given f(x) > 0 with f ′(x) < 0, and f ″(x) > 0 for all x in the interval [0, 2] with f(0) = 1 and f(2) = 0.2, the left, right, trapezoidal, and midpoint rule approximations were used to... more
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04/20/21

The rate of decay in the mass
The rate of decay in the mass, M, of a radioactive substance is given by the differential equation  , where k is a positive constant. If the initial mass was 100g, then find the expression for the... more
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04/20/21

The slope of the tangent to a curve at any point (x, y) on the curve is negative 1 times x divided by y . Find the equation of the curve if the point (2, -2) is on the curve.
A)x + y = 0B)x2 - y2 = -2C)x2 + y2 = 16D)x2 + y2 = 8I believe the answer is D
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Ap Calculus Calculus Precalculus Calc

04/19/21

The temperature of a cup of coffee varies according to Newton's Law of Cooling
The temperature of a cup of coffee varies according to Newton's Law of Cooling: , where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee... more
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Ap Calculus Calculus Precalculus

04/19/21

Estimate the value of the integral from negative 1 to 3 of x cubed, dx by using the Trapezoidal Rule with n = 4
a)8b)19c)22d)36I think its c
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Ap Calculus Calculus Precalculus Calc

04/19/21

Which of the following differential equations is consistent with the following slope field?
 a) dy/dx = x/(y^2)b)dy/dx = x/yc)dy/dx=x^2/yd)dy/dx=x^2/y^2
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04/19/21

The slope of the tangent to a curve at any point (x, y) on the curve is x divided by y . Find the equation of the curve if the point (2, -3) is on the curve.
A) x2 + y2 = 13 B) x2 + y2 = 25 C) x2 - y2 = -5 D) x2 - y2 = 5
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Ap Calculus Calculus Precalculus Calc

04/19/21

The Rate of Decay
 The rate of decay in the mass, M, of a radioactive substance is given by the differential equation  , where k is a positive constant. If the initial mass was 200g, then find the expression for the... more
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04/19/21

Find the particular solution to y ' = sin(x) given the general solution is y = C - cos(x) and the initial condition y of pi over 2 equals 1
a) -cos(x) b) 2 - cos(x) c) -1 - cos(x) d) 1 - cos(x)
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Ap Calculus Calculus Precalculus

04/19/21

What is the integral of lim n→∞ 1/n ∑top: n bottom: i=1 Sqrt[(ln(1+i/n)]?
Hi, had this question:What is the integral of lim n→∞ 1/n ∑top: n bottom: i=1 Sqrt[(ln(1+i/n)]?
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Ap Calculus Calculus Precalculus

04/19/21

If f′′(x)=9e3x+4cos2x, f(0)=3 and f′(0)=13, find f(x).
If f′′(x)=9e3x+4cos2x, f(0)=3 and f′(0)=13, what is f(x).
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Ap Calculus Calculus

04/19/21

How much water, to the nearest gallon, is in the tank at time t = 10 minutes (calculus help please)
Water flows into a tank according to the rate  , and at the same time empties out at the rate  , with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in... more
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Ap Calculus Calculus

04/19/21

growth rate help calculus
Show that f(x) = 2000x^4 and g(x) = 200x^4 grow at the same rate.
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Ap Calculus Calculus

04/18/21

help with calculus
Show that f(x) = 2000x^4 and g(x) = 200x^4 grow at the same rate.
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Ap Calculus Math Calculus

04/16/21

Find the interval of convergence for the summation from n equals 1 to infinity of the quotient of x to the nth power and the product of n and 2 raised to the nth power .
Find the interval of convergence for  .
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Ap Calculus Math Calculus Precalculus

04/15/21

Differentiate each function. Express your answer in a simplified factored form. Please show all the steps.
Differentiate each function. Express your answer in a simplified factored form a) f(x) = (x + 4)3(x - 3)6 What I did: = 3·1(x + 4)2 (x - 3)6 + (x + 4)3 · 6·1 (x - 3)5 ANSWER: 3(x + 4)2 (x - 3)6... more
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