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25,270 Answered Questions for the topic calculus

Calculus

12/30/23

Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(9) − f(4)?

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Calculus Math Statistics

12/29/23

Find the smallest number n of terms needed to obtain an approximation of the series ∞∑k=1 3/k^3, accurate to 10^-6

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Calculus Math Statistics

12/29/23

Estimate the error in using the partial sum of 65 terms of the series ∞∑k=1 9/k^2

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Calculus Math Geometry

12/29/23

Compute the volume of a 3-d object with a trapezoidal base (the base's vertices are (0,0), (6,3), (6,-3), (9,3) & (9,-3)), given that perpendicular cross sections are squares.

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Answers •3

Calculus Math Geometry

12/29/23

Find the surface area of revolution about the x-axis of y=7sin(7x) over the interval 0 <= x <= pi/7

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Calculus Math Geometry Physics

12/26/23

Find the surface area of revolution about the x-axis of y=6x+6 over the interval 0 <= x <= 2

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Calculus Math Geometry Physics

12/25/23

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2 , y=0, and x=3, about the y-axis.

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Calculus Math

12/24/23

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2 , y=0, and x=7, about the y-axis.

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Calculus Math

12/24/23

The region bounded by f(x)=-1x^2+4x+12, x=0, and y=0 is rotated about the y-axis. Find the volume of the solid of revolution.

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Answers •2

Calculus Math

12/24/23

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=9√y and on the left by the y-axis for 0 ≤ y ≤3, about the x-axis.

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Answers •2

Calculus Math

12/24/23

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=4/y and on the left by the y-axis for 2 ≤ y ≤7, about the x-axis.

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Calculus Math

12/24/23

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the graphs of y=x, y=7-x, and the x-axis about the x-axis.

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Calculus Math

12/24/23

Use cylindrical shells to find the volume of the solid generated by rotating the curve y=4ln(x) about the x-axis for 1 ≤ x ≤ e.

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Calculus Math Geometry

12/24/23

Suppose that R is the finite region bounded by f(x)= √x and g(x)= x/3. Find the object's exact volume when rotating R about the x-axis. Find the exact volume when rotating R about the y-axis

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Answers •2

Calculus Math Geometry

12/24/23

Suppose that R is the finite region bounded by y=x, y=x+2, x=0 and x=3. Find the exact value of the volume of the object we obtain when rotating R about the x-axis.

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Calculus Math Geometry

12/23/23

Find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 & y=1 about y=3

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Calculus Math Sat Math Differential Equations

12/22/23

Basic partial derivative verification question

I have F=y'(1+x2y'), and I need to find ∂F/∂y and ∂F/∂y'The answer I get for ∂F/∂y is 0, which is the correct one. However for ∂F/∂y' I should get 1+2x2y', but for some reason I get 1+2x2y'+y'x2.... more

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Calculus Math Geometry

12/22/23

A ball of radius 14 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.

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Answers •3

Calculus Math

12/22/23

Find the volume formed by rotating about the y-axis the region enclosed by: x=4y and y^3=x with y>=0

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Calculus Math

12/22/23

Find the area of the region bound by the curves 2y= 4√x , y=3 & 2y+1x=5

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Answers •3

Calculus Math

12/22/23

Integrating with Respect to Y to find the Area Between 2 Curves Problem

Goal: Find the area of the region enclosed by y=2.25x and x=4--y2 by integrating with respect to y.A) First find the y coordinates of the two points where y=2.25x meets x=4--y2B) Integrate using... more

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Answers •1

Calculus Math Sat Math Act Math

12/21/23

Solving a tricky integral in a simple way

I've been told that this tricky integral is fairly easy to solve with Laplace transform:However, I am not sure on the solution itself after taking the Laplace transform of the integral. Could... more

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Answers •2

Calculus Math

12/21/23

There is a line through the origin that divides the region bounded by the parabola y = 2x - 4x^2 and the x-axis into two regions with equal area. What is the slope of that line?

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Calculus Math

12/21/23

solve for the max area of a rectangle inscribed in a circle with a radius of 8

thanks !

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Answers •2

Calculus Math Sat Math Differential Equations

12/20/23

Solving an interesting integral using residue

I have this interesting integral to solve using residues. So far I have only noted that cos(x)=Re(eix), but I can't seem to arrive at the full solution. I would appreciate any help.

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Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(9) − f(4)?

Find the smallest number n of terms needed to obtain an approximation of the series ∞∑k=1 3/k^3, accurate to 10^-6

Estimate the error in using the partial sum of 65 terms of the series ∞∑k=1 9/k^2

Compute the volume of a 3-d object with a trapezoidal base (the base's vertices are (0,0), (6,3), (6,-3), (9,3) & (9,-3)), given that perpendicular cross sections are squares.

Find the surface area of revolution about the x-axis of y=7sin(7x) over the interval 0 <= x <= pi/7

Find the surface area of revolution about the x-axis of y=6x+6 over the interval 0 <= x <= 2

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2 , y=0, and x=3, about the y-axis.

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2 , y=0, and x=7, about the y-axis.

The region bounded by f(x)=-1x^2+4x+12, x=0, and y=0 is rotated about the y-axis. Find the volume of the solid of revolution.

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=9√y and on the left by the y-axis for 0 ≤ y ≤3, about the x-axis.

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=4/y and on the left by the y-axis for 2 ≤ y ≤7, about the x-axis.

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the graphs of y=x, y=7-x, and the x-axis about the x-axis.

Use cylindrical shells to find the volume of the solid generated by rotating the curve y=4ln(x) about the x-axis for 1 ≤ x ≤ e.

Suppose that R is the finite region bounded by f(x)= √x and g(x)= x/3. Find the object's exact volume when rotating R about the x-axis. Find the exact volume when rotating R about the y-axis

Suppose that R is the finite region bounded by y=x, y=x+2, x=0 and x=3. Find the exact value of the volume of the object we obtain when rotating R about the x-axis.

Find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 & y=1 about y=3

Basic partial derivative verification question

A ball of radius 14 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.

Find the volume formed by rotating about the y-axis the region enclosed by: x=4y and y^3=x with y>=0

Find the area of the region bound by the curves 2y= 4√x , y=3 & 2y+1x=5

Integrating with Respect to Y to find the Area Between 2 Curves Problem

Solving a tricky integral in a simple way

There is a line through the origin that divides the region bounded by the parabola y = 2x - 4x^2 and the x-axis into two regions with equal area. What is the slope of that line?

solve for the max area of a rectangle inscribed in a circle with a radius of 8

Solving an interesting integral using residue

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