25,270 Answered Questions for the topic calculus

Calculus Math

06/27/24

Consider the definite integral Z 1 0 e^4x^2 dx. Evaluate using the Simpson’s rule (n = 8), and using the Trapezoidal rule (n = 7). show all work
Consider the definite integral Z 1 0 e^4x^2 dx. Evaluate using the Simpson’s rule (n = 8), and using the Trapezoidal rule (n = 7). Show all work
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Calculus Math

06/27/24

Use the fundamental theorem of Calculus to find the derivative of the following function. F (x) = Z √x x et(sin t + t2) dt
F(x) = Z √x x e^t(sin t + t^2) dt
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Calculus Math

06/27/24

How much money should be deposited in a bank paying a yearly interest rate of 2.75% compounded monthly so that after 10 years the accumulated amount will be 50, 000?
show all work.
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Calculus

06/27/24

the Rings of Neptune. Recent observations of Voyager I and II showed that Neptune’s ring system is more complex than had been believed.

For one thing, it is made up of a large number of distinguishable rings rather than one continuous great ring as was previously though. The outermost ring, 1989N1R, has an inner radius of... more
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Calculus

06/25/24

Differentials question

I'm not even sure where to start with this one, I've been trying to find dT first but I'm not sure what to do after.The total stopping distance T of a vehicle is shown below, where T is in feet... more
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Calculus Math

06/25/24

The total worldwide box-office receipts for a long-running movie are approximated by the function T(x) = 100x^2 / x^2 + 25
where T (x) is measured in millions of dollars and x is the number of years since the movie’s released. Sketch the graph of the function T and interpret your results. find critical points, the... more
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Calculus Math

06/25/24

An economist had determined that a certain country’s gross domestic product (GDP) is approximated by the function f (x) = 540x1/3
f(x) is measured in billions of dollars and x is the capital outlay in billions of dollars. Use differentials to estimate the change in country’s GDP if the country’s capital expenditure changes... more
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Calculus

06/25/24

A wire of length 100 meters is cut into two parts. One piece is bent into a circle, and the other is bent into a square

The goal is to determine how to cut the wire in order to obtain the maximum total area of the two figures. set up a mathematical function (specify its domain) whose maximum value in its domain... more
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Calculus

06/25/24

The oxygen content t days after organic waste was dumped into a pond is given by f (t) = 100 (t2 + 10t + 100/t2 + 20t + 100).

A) use the intermediate value theorem to conclude that the oxygen content of the pond must have been at a level of 85 % at some time. B) At what time(s) is the oxygen content at the 85% level
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Calculus

06/25/24

Calc 1 Optimization Question
Find the point on the graph of the function that is closest to the given point.f(x) = (x-1)^2Point: (-5,3)
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Calculus

06/25/24

calculate the amount of work required to pull a spring 1 foot beyond its rest length, if the force required to do so is 6 pounds.
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Calculus

06/24/24

Find the maximum and minimum values of the function g(θ)= 7(θ)- 9sin(θ) on the interval (0,pi)
I have been working on this question for about an hour, but keep getting it wrong.. I don't know what I am doing wrong. Please help!
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Calculus

06/23/24

Find an antiderivative of in the variable x where x != 0
Find an antiderivative of  3x^2+7x^4/x^5 in the variable x where x ≠ 0Remember to include a "+ C" if appropriate. Antiderivative = 
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Calculus

06/22/24

Compute the length of the curve
Compute the length of the curve over the given interval. r(t) =  2t, ln(t), t2 ,    1 ≤ t ≤ 3
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Calculus

06/22/24

Arc length of the curve
Find the arc length of the curve on the interval. r(t) =  t2 + 1, 8t3 + 7 , −1 ≤ t ≤ 0
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Calculus

06/21/24

Area of a surface of Revolution
The given curve is rotated about the y-axis. Find the area of the resulting surface.x2⁄3 + y2⁄3 = 4,    0 ≤ y ≤ 8
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Calculus

06/21/24

Area of a surface of Revolution
If the infinite curve y= e^-8x, x ≥ 0 is rotated about the x-axis. Find the area of the resulting surface.
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Calculus Math

06/20/24

Calculus Optimization Problem
Find the maximum area of a rectangle in the first quadrant under the function y=3e-x/2.
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Calculus

06/18/24

Find the spherical coordinates

The rectangular coordinates (x, y, z) of a point are given. Find the spherical coordinates (𝜌, 𝜃, φ) of the point. Express the measure of the angles in degrees rounded to the nearest integer.... more
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Calculus

06/16/24

Calculus help question
Find an antiderivative F(x) with F′(x)=f(x)=5+28x3+21x6 and F(1)=0. Remember to include a "+ C" if appropriate.
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06/15/24

Plane Curve with Given Curvature
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Calculus

06/15/24

Cross product u ✕ v finding obtuse angle
Use the cross product u ✕ v to find the obtuse angle between vectors u and v, where u = −i + 4j + k and v = i − 3j. Express the answer in degrees rounded to the nearest integer.
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Calculus

06/15/24

Magnitude of the torque
A mechanic uses a 12 in wrench to turn a bolt. The wrench makes a 30° angle with the horizontal. If the mechanic applies a vertical force of 14 lb on the wrench handle, what is the magnitude of the... more
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Calculus

06/12/24

Help with critical points and extrema problem (calculus)
The surface area of a cell in a honeycomb is given by the following, where h and s are positive constants and 𝜃 is the angle at which the upper faces meet the altitude of the cell (see figure).S =... more
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Calculus

06/12/24

Critical Points question Calc 1
Find the critical numbers of the function. (Enter your answers as a comma-separated list.)f(𝜃) = 10sec 𝜃 + 5tan 𝜃,    0 < 𝜃 < 2𝜋
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