Find the limit as x approaches -3 of (x^2+x-6)/(x+3)
-5
100
Find the average velocity of a ball with the position s(t)=-16t^2+100 over the interval [1,2].
-48 ft/sec
100
Find the critical points of the function f(x)= x^2(x-3).
x=0,2
100
Determine the open interval in which the function of f(x)=x^3-12x is concave down.
(-infinity, 0)
100
Suppose x and y are both differentiable functions of t and are related by the equation y=x^2+3. Find dy/dt when x=1 given that dx/dt=2 when x=1.
4
200
Find the limit as x approaches 0 when [(x+1)^(1/2)-1]/x
1/2
200
At time t=0, a diver jumps from a diving board that is 32 ft above the water. The position is given by s(t)=-16t^2+16t+32. When does the diver hit the water?
t=2 sec
200
Determine the absolute maximum of the function
f(x)= -x^2+3x on the interval [0,3].
(3/2, 9/4)
200
Find the points of inflection of f(x)=x^3-6x^2+12x.
x=2
200
A pebble is dropped into a pond causing ripples in the form of concentric circles. The radius of the outer circle is increasing at a constant rate of 1 ft/sec. When the radius is 4 ft, at what rate is the total area of the disturbed water changing?
8(pi)
300
Find the limit as x approaches 0 when (4sinx)/x
4
300
A diver jumps from a diving board has a position modeled by s(t)= -16t^2 + 16t + 32. What is his velocity when he hits the water?
-48 ft/sec
300
Find the open intervals on which f(x)=x^3-(3/2)x^2 is increasing.
(-infinity, 0) U (1, infinity)
300
Determine the open intervals in which the function f(x)=(x^2+1)/(x^2-4) is concave up.
(-infinity, -2) U (2, infinity)
300
Air is being pumped into a spherical balloon at a rate of 4.5 cubic inches per minute. Find the rate of change of the radius when the radius is 2 inches.
0.09 in/min
400
Find the limit as x approaches infinity when (x^2+3)/(x-1)
DNE
400
Find the acceleration of a car with position t^3 + 5t^2 +10 when t = 10.
70
400
Find any critical points of the function f(x)=2x-3x^(2/3) on the interval [-1,3].
x=0,-1
400
Find the points of inflection of f(x)=x^4-4x^3.
x=0,2
400
The equation of a point moving along a graph can be modeled by y=tanx. Find dy/dt when x=-(pi)/3 and dx/dt=2 cm/sec.
8 cm/sec
500
Find the limit as x approaches infinity when (3x+3)/4x
3/4
500
A silver dollar is dropped from the top of a building. Its position can be modeled by s(t)=-16t^2+4t+210. Find its velocity in ft/sec when t=1.
-28 ft/sec
500
Find the open intervals on which f(x)= (x^5-5x)/5 is increasing.
(-1,1)
500
Determine the open intervals in which the function f(x)=x(x-4)^(1/2) is concave down.
(2,4)
500
All edges of a cube are expanding at a rate of 3 cm/sec. How fast is the surface area changing when each edge is 10 cm?