608 Answered Questions for the topic AP Calculus

Ap Calculus

13d

#### The derivative of a function f is given by f′(x)=0.1x+e0.25x . At what value of x for x>0 does the line tangent to the graph of f at x have slope 2 ?

I have homework in AP calculus

#### If the fine imposed is the one needed to motivate the company to cleanup the spill in the specified number of days, and the company hires crews to do that, what would the Cost to the company be?

WHAT YOU KNOW:An oil spill has fouled 400 miles of Pacific shoreline. The company responsible has been ordered to clean the mess. Each clean-up crew costs $14000 to bring in, and $400 per crew per...
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#### If the fine imposed is the one needed to motivate the company to cleanup the spill in the specified number of days, and the company hires crews to do that, what would the Cost to the company be?

WHAT YOU KNOW:An oil spill has fouled 400 miles of Pacific shoreline. The company responsible has been ordered to clean the mess. Each clean-up crew costs $14000 to bring in, and $400 per crew per...
more

06/01/20

#### Fundamental theorem of Calculus

Given that D(t) is a continuous and diffrentiable function . Also D(0) = 0 , D(5) = 120 and D(20) = 200 , simplify the integral using fundamental theorem , ∫ D'(t/4)dt inthe interval 0<t...
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Ap Calculus Calculus

05/11/20

#### Antiderivative Help!

So I am preparing for AP calculus AB exam coming up, and I recently am stuck on this minuscule problem that frequently shows up in other forms. If I am told to Integrate f’’(2x) , what should the...
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#### Calculus help needed pleeease!!

Given f(x) > 0 with f ′ (x) < 0, and f ″(x) < 0 for all x in the interval [0, 1] with f(0) = 1 and f(1) = 0.3, the left, right, trapezoidal, and midpoint rule approximations were used to...
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#### Differential Equation

The differential equation I. produces a slope field with horizontal tangents at x = -4II. produces a slope field with vertical tangents at x = -4III. produces a slope field with columns of...
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#### Calculus help needed

The temperature of a cup of hot tea varies according to Newton's Law of Cooling: , where T is the temperature of the tea, A is the room temperature, and k is a positive constant. If the water cools...
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#### Find the expression for 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 200g, then find the expression for the...
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#### Find the solution

Find the particular solution to y ′ = 2sin(x) given the general solution is y = C − 2cos(x) and the initial condition .Question options:
1)
-2cos(x)
2)
3 - 2cos(x)
3)
2 - 2cos(x)
4)
-1...
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#### Use 6 Trapezoids to estimate Integral

Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of .
x
1
3
4
6
7
9
10
f(x)
4
8
6
10
10
12
16

#### Which are true of the equation

The differential equation .I. produces a slope field with horizontal tangents at y = 2II. produces a slope field with vertical tangents at y = 2III. produces a slope field with columns of parallel...
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#### Which are true for the equation

The differential equation I. will produce a family of quadratic functions.II. will produce a family of linear functions.III. will produce a family of exponential functions.Question options:
1)
I...
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#### Table for differential equation

Choose the appropriate table for the differential equation .Question options:1)
x
0
0.5
2
0
undefined
2)
x
0
0.5
2
undefined
-1
undefined
3)
x
0
0.5
2
0
-3
0
4) Cannot be found...
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#### Differential Equation

The differential equation . I. will have a slope field with negative slopes in quadrant III. will have a slope field with positive slopes in all quadrantsIII. will produce a slope field with...
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#### Differential Equation

The differential equation . I. produces a slope field with horizontal tangents at y = 4II. produces a slope field with horizontal tangents at x = 0III. produces a slope field with vertical...
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#### Please help, I am stuck...

Find F ′(x) for .Options:
1)
sin(24) - sin(x12)
2)
sin(x7)
3)
-sin(x12)
4)
-3x2sin(x12)

#### Plese help, I am stuck...

Which of the following shows that f(x) grows faster than g(x)? Options:
1)
2)
3)
4)
None of these

#### Please help, I am stuck...

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Approximation, using the 4...
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#### Really need someone's help with calculus

The slope field for a differential equation is shown in the figure. Determine the general solution of this equation.Options:
1)
y=Cx2
2)
x=Cy2
3)
y2 - x2 = C2
4)
x2 + y2 = C2

#### Assistance with math please?

Find the domain for the particular solution to the differential equation , with initial condition y(2) = 2.Options:
1)
x > -2
2)
3)
[-4, 4]
4)
All real numbers

#### Hello! I need assistance with math. Thank you a lot

Find the average value of , on its domain.Options:
1)
2π
2)
4π
3)
2
4)
4

#### Really really need assistance and help. Thank you in advance..

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units....
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#### Really really need assistance and help. Thank you in advance..

Use geometry to evaluate where .

#### Please help! I am stuck with this homework problem..

Show that the function is constant on the interval (0, +∞).

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