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....
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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...
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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...
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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
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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 =...
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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...
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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...
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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....
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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...
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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...
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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...
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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...
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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:...
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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....
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