Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.
1/(80pi) cm/min
100
Suppose you have a 10'x20' piece of cardboard. If you wanted to make an open rectangular box (by cutting out the corners and folding up the sides), a) what dimensions would create a box with the largest volume?
15.8 by 5.9
100
Derivative of sin(x)cos(x)tan(x)
2sin(x)cos(x)
100
lim as x approaches .1 of sin(x)/x
DNE
100
Find the derivative of x^2 +15x + cos(x) using the limit definition
2x +15 - sin(x)
200
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 theta = .5 radians?
.311 ft/min
200
The quantity Q = 2x2 + 3y2 is subject to the constraint x + y = 5. What is the minimum quantity of Q?
30
200
Find the derivative of f(w) = sin(w) +w^2 * tan^-1(w)
cos(w) + 2wtan^-1(w) + w^2/(1+w^2)
200
lim as x approaches 0 of (sin(x) * cos(4x)) / (x + xcos(5x))
1/2
200
lim as x approaches 3 of (sqrt(3x+16)-5)/(x^2-3x)
1/10
300
Two people on bikes are separated by 350 meters. Person A starts riding north at a rate of 5 m/sec and 7 minutes later Person B starts riding south at 3 m/sec. At what rate is the distance separating the two people changing 25 minutes after Person A starts riding?
8 m/sec
300
Suppose you have a 10'x20' piece of cardboard. If you wanted to make an open rectangular box (by cutting out the corners and folding up the sides), what is the largest volume?
195.8 cubic feet
300
Suppose f(x) is twice differentiable function satisfying f(x^2) = f(x) + x^2. What are f'(1) and f"(1)?
2 and -2/3
300
lim as x approaches 0 of sin(x)/(x^(1/3))
0
300
lim as x approaches 0 from the left of (x^3 - 5x^2 + 6x) / ( x^4 - 4x^2)
infinity
400
A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?
48/13 ft/sec
400
A farmer is going to build a pen using 240 feet of wood. One side of the pen will border a barn, and there will be a wooden divider to separate the pen into 2 parts. What is the maximum possible area of the pen?
4800 sq ft
400
Differentiate exp(sin(exp(x)))
cos(exp(x))exp(sin(exp(x))+x)
400
lim as x approaches 0 of sin(6x) / sin(4x)
3/2
400
Let f (x) = 2sqrt(x) . Find a value for delta such that
if |x - 1| < delta , then |f(x) - 2| < 1/2 .
delta = 7/16
500
A trough of water is 8 meters deep and its ends are in the shape of isosceles triangles whose width is 5 meters and height is 2 meters. If water is being pumped in at a constant rate of 6 m^3/s . At what rate is the height of the water changing when the water has a height of 120 cm?
.25 m/s
500
You're contracted to build a square-based 600 cubic foot container made of steel. Assuming the construction is an open-top container, a) what are the dimensions of the container that will minimize the weight
10.63*10.63*5.31
500
Find f'(3pi/2) for f(x) =(sin(x) +1)^x
0
500
Prove lim as x approaches 0 sin(x)/x = 1 w/o L'Hopitals
Did you do it??
500
Let f(x) = 5x-2. Use the epsilon delta definition of a limit to prove that lim as x approaches 4 of f(x) = 18