Derivatives
5x2
What is 10x?
lim x-2 (8−3x+12x2)
What is 50?
lim x-2 x3−7x2+10x/x2+x−6
What is 6/-5?
A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m2/sec at what rate is the radius decreasing when the area of the sheet is 12 m2?
What is −0.040717?
The integral of ex
What is ex+C?
2t4−10t2+13t
What is 8t3−20t+13?
lim x-(-3) 6+4t/t2+1
What is -3/5?
Rolle's Theorem
What is "if a function is continous and differentiable on the interval (a,b), and f(a)=f(b), then there is a point where f'(c)=0"?
A person is standing 350 feet away from a model rocket that is fired straight up into the air at a rate of 15 ft/sec. At what rate is the distance between the person and the rocket increasing 20 seconds after liftoff?
What is 9.76187?
∫6x5−18x2+7 dx
What is x6−6x3+7x+C?
(y−4)(2y+y2)
What is 3y2−4y−8?
lim t-(-1) t+1/|t+1|
What is dne?
Derive: (6x2+7x)4
What is 4(12x+7)(6x2+7x)3?
The radius of a sphere is increasing at a rate of 0.50 centimeters per minute.
At a certain instant, the radius is 17 centimeters.
What is the rate of change of the volume of the sphere at that instant?
What is 578pi?
∫10w4+9w3+7w dw
What is 2w5+9/4w4+7/2w2+C?
Find the slope of the line tangent to
g(x)=16/x−4√x when x=4.
What is -2?
h(z)=
6z, z≤−4
1−9z, z>−4
lim h(z) x-(-4)
What is DNE?
Derive: x2+y3=4
What is y'=−2x/3y2?
The radius of the base of a cone is decreasing at a rate of 2 centimeters per minute.
The height of the cone is fixed at 9 centimeters.
At a certain instant, the radius is 13 centimeters.
What is the rate of change of the volume of the cone at that instant?
What is -156pi?
∫10t-3+12t-9+4t3 dt
What is −5t-2−3/2t-8+t4+C?
The position of an object at any time t is given by s(t)=3t4−40t3+126t2−9. When is the object moving to the left?
What is −∞<t<0 and 3<t<7?
lim x-0 x/3−√x+9
What is -6?
Conditions for continuity.
What is, "a function is continous at point (a,b) if:
- f(a) is defined
- the limit as x approaches a of f(x) exists (the limits from both sides are equal)
- the limit as x approaches a of f(x)= f(a)
The radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second.
The height of the cylinder is fixed at 2.5 kilometers.
At a certain instant, the radius is 40 kilometers.
What is the rate of change of the volume of the cylinder at that instant?
What is -2400pi?
1/x