25,270 Answered Questions for the topic calculus

Calculus Math

04/22/24

Find the Arc-length of the curve: y=1/3x^3/2 - x^1/2 ; 1 ≤ x ≤ 9

Find the Arc-length of the curve: y=1/3x3/2 - x1/2 ; 1 ≤ x ≤ 9If possible please explain the step by step process in a video.
Calculus Math

04/22/24

Draw the graphs of y= 8cos(x) , y = sec^2(x) on the interval [-π/2, π/2]. Answer parts ABC below.

Draw the graphs of y= 8cos(x) , y = sec^2(x) on the interval [-π/2, π/2]. Answer parts ABC below.A). What are the points of intersection?B). The enclosed region is rotated around the line x = π/2.... more
Calculus Math

04/22/24

The region encoded by: x = y^2 and y = x-2 is revolved around the line x= -3. Solve all the parts below

The region encoded by: x = y2 and y = x-2 is revolved around the line x= -3. Solve all the parts belowA). Find the points of intersection algebraicallyB). Draw the pictureC). Write an integral... more
Calculus

04/21/24

use the shell method to find the volume of region enclosed by y=x, y=-x+1, revolved about the line x=2

Sketch and find the volume, using the shell method, of the region enclosed by y=x, y=-x+1, revolved about the line x=2.
Calculus

04/21/24

Use disk method to find volume of region enclosed by y=x, y=-x+1, revolved around y-axis

sketch the graph and find the volume, using the disk method, of the region enclosed y=x, y=-x+1, revolved about the y-axis.
Calculus

04/20/24

Evaluate I= int(sinx+4y)dx + (4x+y) dy for the nonclosed path ABCD

A = (0,0)B = (4,4)C = (4,8)D = (0,12)
Calculus

04/19/24

Find the work done in pumping the water over the rim of a tank that is 50 feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 7 feet.

Find the work done in pumping the water over the rim of a tank that is 50 feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 7 feet.not sure if i did it... more
Calculus

04/19/24

(i) Find an expression for the sum of the series ∑ r=0 ∞ ​ x r . State the interval of convergence for the series. (ii) Hence, USING SIGMA NOTATION, deduce a series for:

(i) Find an expression for the sum of the series ∑r=0∞ ​x^r. State the interval of convergence for the series. (ii) Hence, USING SIGMA NOTATION, deduce a series for: (a) 1/1+x^2​ (b) arctanx (c) 6/π​ more
Calculus

04/19/24

If cos 𝜃 = − (1/4) and 𝜃 is in III quadrant. Find the exact value of a) cos 𝜃/2 b) csc 2𝜃

If cos 𝜃 = − (1/4) and 𝜃 is in III quadrant. Find the exact value of a) cos 𝜃/2 (2) b) csc 2𝜃
Calculus

04/18/24

Absolute Maximum value on a closed interval

The figure below shows the graph of f ′, the derivative of the function f, on the closed interval from x = −2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x =... more
Calculus

04/18/24

Find the work done (in joules) if the spring is stretched from its natural length to 0.65 meters.

Consider a spring. Recall that the force required to stretch a spring by x units beyond its originallength is given by F(x) = kx, where k is a constant called the spring constant. Suppose a spring... more
Calculus

04/18/24

Find the work done in pumping the water over the rim of a tank that is 50 feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 7 feet.

Find the work done in pumping the water over the rim of a tank that is 50 feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 7 feet.
Calculus

04/17/24

A tank in the shape of a right circular cone is full of water. If the height of the tank is 15 feet and the radius of its top is 6 feet, find the work done

A tank in the shape of a right circular cone is full of water. If the height of the tank is 15 feet and the radius of its top is 6 feet, find the work done in (a) pumping the water over the top... more
Calculus

04/17/24

A rectangular tank that is 6 feet long, 9 feet wide and 6 feet deep is filled with a heavy liquid that weighs 120 pounds per cubic foot.

A rectangular tank that is 6 feet long, 9 feet wide and 6 feet deep is filled with a heavy liquid that weighs 120 pounds per cubic foot. In each part below, assume that the tank is initially full.... more
Calculus

04/17/24

Find the amount of work (in Joules) required to empty the trough by pumping the water over the top.

A trough is 2 meters long, 3 meters wide, and 3 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isosceles triangle (with height 3 meters, and base, on... more
Calculus

04/17/24

Find the work done in pumping the water over the rim of a tank that is 50 feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 4 feet.  

Find the work done in pumping the water over the rim of a tank that is 50 feet long and has a semicircular end of radius 10 feet if the tank is filled to a depth of 4 feet.  _______ foot-pounds
Calculus

04/17/24

What is the force (in Newtons) that holds the spring stretched at the same distance (13 cm)?

Work of 4 Joules done in stretching a spring from its natural length to 13 cm beyond its natural length. What is the force (in Newtons) that holds the spring stretched at the same distance (13... more
Calculus

04/17/24

How much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet beyond its natural length? foot-pounds

A force of 3 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet... more
Calculus

04/17/24

find the work done in stretching the spring from its natural length to a length of 0.5 meters. 

If the natural length of a spring is 0.4 meter, and if its takes a force of 14 newtons to keep it extended an additional 0.05 meters,find the work done in stretching the spring from its natural... more
Calculus

04/17/24

Use differentiability of power series to find the sum

Use differentiability of power series to find the sum (n=1 and inf on sum sign) ∑ (x2n)/n within its radius of convergence.

04/17/24

Use differentiability of power series to find the sum

Use differentiability of power series to find the sum (n=1 and inf on sum sign) ∑ (x2n)/n within its radius of convergence.
Calculus

04/17/24

Calculus 3 question

The velocity function for a moving object is 𝐯(𝑡) = <−2𝑡+9, (7−𝑡)^3/2, 1/3 t^2 - t >, where distances are in centimeters and time is in seconds. Find the following:a). The function’s domain:... more
Calculus

04/16/24

Need help with Euler's method

Use Euler's method with step size 0.5 to compute the approximate y=values y1,y2,y3, and y4 of the solution of the initial-value problem y'=y-2x, y(1)=0
Calculus

04/16/24

Need help with a differential equation!

Verify that y=-tcos(t)-t is a solution of the initial-value problem, t(dy/dt)=y+t2sin(t), y(pi)=0

04/16/24

Application of Antiderivatives in PVA (position, velocity, acceleration)

A child throws a ball straight up. If the ball is to reach a height of 9.8m, what is the minimum initial velocity that must be imparted to the ball? Assume the initial height of the ball is 1m.... more

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