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Derivatives
Integrals
Related Rates
Limits
Area Between Curves & Volumes
100
The derivative of 2x^5
What is 10x^4
100
The integral of x^3 + 5
What is (x^4)/4 + 5x
100
Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.
What is (1/80pi)
100
lim as x approaches 3 of (x^2 + 9)/(x+3)
What is -6
100
Find the volume of a solid by rotating the region bounded by the curve y=2x-x^2 and y=0 about the line x=3 using cylindrical shell method
What is (56pi)/3
200
derivative of (cos(x^3))^2
What is -6x^2cos(x^3)sin(x^3)
200
Integral from -3 to 1 of 6x^2-5x+2
What is 84
200
Air is being pumped into a spherical balloon such that its radius increases at a rate of .75 in/min. Find the rate of change of its volume when the radius is 5 inches.
What is 75(pi) cu in/min
200
lim sin(x)/x
What is 1
200
Find the volume of the solid obtained by rotating the region bounded by y=4x-x^3 and y=0 and the lines x=0 and x=2 about the y-axis using the method of cylindrical shells
What is (128pi)/15
300
Derivative of sin(5x)
What is 5cos(5x)
300
Integral from pi/6 to pi/4 of 5-2secxtanx
What is (5pi/12) - 2(sq root 2) + (4/(sq root 3))
300
A car is traveling north toward an intersection at a rate of 60 mph while a truck is traveling east away from the intersection at a rate of 50 mph. Find the rate of change of the distance between the car and truck when the car is 3 miles south of the intersection and the truck is 4 miles east of the intersection.
What is 4 mph
300
lim as x approaches infinity of (1/x)
What is 0
300
Find the area of the region bounded by y=(sq root of x) and y=x^3
What is 5/12
400
derivative of 6x^(3/2)tanx
What is 3x^(1/2)(2(secx)^2+3tanx)
400
Integral from 0 to 3 of the absolute value of (3x-5)
What is 41/6
400
A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of ft/sec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?
What is 0.1319 ft/sec
400
lim as x approaches 4 of (x^2-7x+12)/(x-4)
What is 1
400
Find the volume of the solid obtained by rotating the region bounded by x=y^2 - 2 and y=x about the line y=3
What is (45pi)/2
500
derivative of x^3 lnx
What is (x^2(1+3lnx))
500
Integral from 0 to 1 of 4x - 6 (cube root (x^2)) dx
What is -8/5
500
Two people are 50 feet apart. One of them starts walking north at a rate so that the angle shown in the diagram below is changing at a constant rate of 0.01 rad/min. At what rate is distance between the two people changing when radians?
What is 0.311 ft/min
500
lim as x approaches 2 of k(x) k(x) = x^2 + 9 when x<2 k(x) = x^2 - 3 when x >/= 2
What is dne
500
Find the volume of the solid formed by rotating the region bounded by y=(x-1)(x-3)^2 and the x-axis about the y-axis
What is (24pi)/5