Limits
What is the limit as x approaches 5 of the function y = 3x2?
75
What is the derivative of the function y = x2(2x4-5)?
12x5-10x
What is the derivative of the function y = (x3 + 3)5?
15x2(x3 + 3)4
y = x3 + 4x2
What is the x-coordinate of the relative maximum on the interval (-5,0)?
-8/3
The radius of a circular puddle is growing at a rate of 10 cm/sec. How fast is its area growing when the radius is 14 cm?
280(pi) cm2/sec
What is the function as x approaches infinity of the function y = 1/x?
0
What is the derivative of the function y = (1 + x3/2)(x-3 - 2x1/3)?
-3x-4 - (3/2)x-5/2 - (2/3)x-2/3 - (11/3)x5/6
What is the derivative of the function y = (5x2 + 3)4?
40x(5x2 + 3)3
y = x4 - 2x3
For what value of x does f have a relative minimum?
3/2
A sphere-shaped balloon is being inflated so that its diameter is increasing at a rate of 2.9 cm/min. How quickly is the volume of the balloon increasing when the diameter is 17 cm?
(1445/4)pi cm3/min
What is the limit as x approaches infinity of the function f(x) = (2x2+3) / (x2-5x-1)?
2
What is the derivative of the function f(x) = (2x2) / (3x+1)?
What is the derivative of the function f(x) = (3x - 1)(-3x2 - 4)-3?
3(15x2 - 6x - 4) / (-3x2 - 4)4
y = x3 - 3x2 + 6
For what value(s) of x does f have a relative maximum?
0
What are two positive numbers with a product of 100 and the smallest sum possible?
10, 10
What is the limit as x approaches 3 of the function f(x) = (2x2-5x-3) / (x-3)?
7
What is the derivative of the function f(x) = (sqrt(x) + 2x) / (7x - 4x2)?
(x/2-1/2 + 2)(7x - 4x2) - (x1/2 + 2x)(7 - 8x) / (7x-4x2)
What is the derivative of the function (x2 - 3)1/5 / (-x - 5)?
(3x2 - 10x - 15) / 5(-x - 5)2(x2 - 3)4/5
f(x) = x4 - 2x3
Find the relative extrema of the function.
Relative minimum at (3/2, -27/16)
A farmer is building a fence around a rectangular field that has a river on one of its sides. If he has 2400 ft of fencing and wishes to enclose the largest area possible, what dimensions should he use?
x = 600, y = 1200
What is the limit as x approaches 5 of the function f(x) = (x-5) / (sqrt(x+4)-3)?
6
What is the derivative of the function f(x) = (5x5 - x3 - 4) / (2x2 - 5)?
(30x6 - 127x4 + 15x2 + 16x) / (4x4 - 20x2 + 25)
What is the derivative of the function f(x) = -sin(-9x2 + 3x + 5)?
-cos(-9x2 + 3x + 5)(-18x + 3)
f(x) = 6x5 - 50x3 - 120
For what value(s) of x does f have a relative maximum?
-sqrt(5)
A box is made by cutting square pieces of the same size from the corners of a sheet of cardboard and then folding up the sides. If a square sheet of 20 cm x 20 cm cardboard is used, what are the dimensions of a box with the largest possible volume?
(40/3) cm x (40/3) cm x (10/3) cm