The region between f(x) = 2 + xcosx and the x axis over the interval [-2,2] is revolved around the x axis. Find the volume using disc method.
52.43 units cubed
100
Find Volume when 12(y^2-y^3) is revolved around the x-axis using cylindrical shell method.
Volume: (6pi)/5
100
A hemispherical bowl of radius "a" is filled with water to a depth "h". Find volume of water in bowl.
(pih^2(3a-h))/3
100
lim x-> 2 of (x^2 - 4)/(x-2)
4
200
Find the Linearization of f(x) = x^2 + 3x +1 at x = 2
L(x) = 7x-3
200
The region between the graphs of y = cosx and y = sinx and the y axis is revolved around the x axis. Find the volume of the solid generated using washer method.
pi/2 units cubed.
200
The solid lies between planes perpendicular to the x-axis at x=0 and x=4. The cross sections perpendicular to the x-axis on the interval 0 to 4 are squares whose diagonals run from y=-sqrtx to y=sqrtx. Find volume.
Volume: 16
200
Water runs into hemispherical bowl of radius 5 m at rate of .2 meters cubed per second. How fast is water level rising when water is 4 meters deep?
1/120pi meters per second.
200
Who created the FTC?
Isaac Newton
300
Linear Approximation for Roots and Powers
What is (1+x)^k = 1 + kx
300
Find the volume of the solid generated when the graphs of y = x^3 and y = 4x are revolved around the line y = 8.
832pi/21
300
Find the volume of the solid generated by rotating the finite region bounded by (2x)^(1/2) and 4x^2 about the x axis.
What is 3π/20.
300
Find the volume of a solid generated by rotating the finite region bounded by (5+sin(2πx))^1/2 and (2+cos(2πx))^1/2 over the interval [0,5] about the x-axis.
What is 15π.
300
Derivative of arccos?
-1 / sqrt(1-x^2)
400
Find the Linearization of f(x) = cosx at x = pi/2
L(x) = -x + pi/2
400
Volume of solid generated by revolving the region bounded by y = (x)^1/2, y = 2, and x = 0 about the y axis.
32pi/5
400
Find the Volume of the solid generated by the finite region enclosed by (x^(1/2)) and x^3 about the x-axis.
What is 5π/14.
400
Build a rectangular pen with three parallel partitions using 500 feet of fencing; What dimensions maximize the area and what is the area generated with these dimensions?
What is 50 feet and 125 feet. Area = 6250 ft^2.
400
Find the inverse of the derivative of f(x) = x^3 +7x +2. Then, find the equation of the tangent line to the inverse at (10,1)
Derivative of Inverse: 1/(3y^2 + 7)
Tangent line: y = (1/10)x
500
f is a function with f(0) = 1 and f'(x) = cos(x^2), find the linearization of f at x = 0 and estimate the value of f at x = 0.1
L(x) = x + 1 and f(0.1) = 1.1
500
Volume of bowl created by revolving graph of y = .5x^2 between y = 0 and y = 5 about the y axis. If filled at rate of 3 cubic units per second, how fast is water level rising when water is 4 units deep?
Volume: 25pi
Rate: 3/(8pi)
500
Find the volume of the solid generated by rotating the finite region bounded by (x^2+(x^9)sin(8πx^5))^1/2 and (x^8+(x^9)sin(8πx^5))^1/2 on the interval [0,1] about the x-axis.
What is 2π/9.
500
A container in the shape of a right circular cylinder with no top has surface area 3 ft.2 What height h and base radius r will maximize the volume of the cylinder and what is this volume?
What is radius = 1 ; height = 1; Volume = π^3
500
This theorem states that an indefinite integral can be reversed by differentiation.