1,126 Answered Questions for the topic AP Calculus

Ap Calculus Math Calculus

02/01/21

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum...
The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the... more
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Ap Calculus Math Calculus

02/01/21

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Find the average rate of change of f(x) over the interval [3, 13]
The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Find the average rate of change of f(x) over the interval [3,... more
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Ap Calculus Math Calculus

01/31/21

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the...
The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the... more
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Ap Calculus Math Calculus

01/31/21

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. Using a right Riemann sum with 5 subintervals...
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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Ap Calculus Math Calculus

01/31/21

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1).

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1)f(x) and g(x) are a... more
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Ap Calculus Math Calculus

01/31/21

f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives values of f '(x). What is the value of g '(0.1)?

f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives values of f '(x). What is the value of g '(0.1)? f '(x) 1 2 3 -4 5 x 0.1 ... more
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Ap Calculus Math Calculus Precalculus

01/29/21

I need help with integrals
Let f be the function given by f(x)=sin^2(x/4)e^(−x2). It is known that (top value= π/2)∫(bottom value=0) f(x) dx= 0.0223. If a midpoint Riemann sum with two intervals of equal length is used to... more
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Ap Calculus Math Calculus Precalculus

01/29/21

need help with math
x | 2 | 4 | 6 | 7 | 11-----------------------------------------------------------------------------------f(x) | 0.7 | 1.1 | 1.9 | 2.5 | 5.3The continuous function f is known to be... more
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Ap Calculus Math Calculus Precalculus

01/28/21

Population Density and Area
Which has more people, Country A with an area of 98 miles2 and a population density of 49 people/kilometers2 , or Country B with an area of 49 kilometers2 and a population density of 98 people/miles2? more
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Ap Calculus Math Calculus Ap Math

01/27/21

Please leave your answer in sigma notation, and give the interval of convergence.
Find the Taylor series for the following functions. You do not need to use the definition, i.e., feel free to use any known series as a template for your answer. Please leave your answer in sigma... more
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Ap Calculus Math Calculus Ap Math

01/27/21

Give the Maclaurin series representation (either in sigma notation, or the first four terms) and the interval of convergence for the following functions.
Give the Maclaurin series representation (either in sigma notation, or the first four terms) and the interval of convergence for the following functions.a) e^xb) cos(x)c) tan^(-1) (x)d) ln(1+x)
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Ap Calculus Math Calculus Ap Math

01/27/21

Using the definition, find the Taylor series of sin(x) centered at x=pi/2
Using the definition, find the Taylor series of sin(x) centered at x=pi/2. Show the first five derivatives and how they are used to find the coefficients of the series. Write your final answer in... more
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Ap Calculus Math Calculus

01/27/21

Which of the following functions grows the slowest as x goes to infinity?

Which of the following functions grows the slowest as x goes to infinity? A xe B ex C ex D They all grow at the same rate.
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Ap Calculus Math Calculus

01/27/21

Which of the following functions grows at the same rate as ex as x goes to infinity?

Which of the following functions grows at the same rate as ex as x goes to infinity? A ex+3 B e3x C e2x D e-x
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Ap Calculus Math Calculus

01/27/21

What does limit as x goes to infinity of the quotient of f of x and g of x equals 5 show?

What does  show? A g(x) grows faster than f(x) as x goes to infinity. B f(x) and g(x) grow at the same rate as x goes to infinity. C f(x) grows faster than g(x) as x goes to... more
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Ap Calculus Math Calculus

01/27/21

Compare the rates of growth of f(x) = the square root of x and g(x) = Ln(x) as x approaches infinity.

Compare the rates of growth of f(x) =  and g(x) = Ln(x) as x approaches infinity. A f(x) grows faster than g(x) as x goes to infinity. B g(x) grows faster than f(x) as x goes to... more
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Ap Calculus Math Calculus

01/27/21

Which of the following functions grows the fastest as x goes to infinity?
Which of the following functions grows the fastest as x goes to infinity? A 2x B 3x C ex D x20
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Ap Calculus Math Calculus

01/27/21

Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is... more
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Ap Calculus Math Calculus

01/26/21

The graph of f "(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is true?

The graph of f "(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is true? A The graph of f has a relative maximum at x = 0. B The graph of f has... more
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Ap Calculus Calculus

01/26/21

Calculus FRQ Help?
A particle moves along the y-axis so that its position at time t is given by y(t)= t2tan(1/t) for t>1.a. Show and explain that the velocity of the particle at time t is given by v(t)= 2ttan(1/t)... more
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Ap Calculus Math Calculus

01/25/21

For what value of b is f continuous at x=2?
f(x)= x2 - 3bx + 2 ; x ≤ 2 2bx2 - 8 ; x > 2
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Ap Calculus Math Calculus

01/24/21

Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y4
Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y4."
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Ap Calculus Math Calculus

01/24/21

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 8 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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Ap Calculus Math Calculus

01/24/21

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of the integral from 1 to 2 of f of x, dx

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of  . Give 3 decimal places for your... more
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Ap Calculus Math Calculus

01/24/21

Solve the differential equation y prime equals the product of 6 times x and the square root of the quantity 1 minus y squared . Explain why the initial value problem y prime equals the product...
Solve the differential equation  . Explain why the initial value problem  with y(0) = 2 does not have a solution.
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