Theorems and Conditions
Pure Pain and Misery
Formulas
What's wrong with this answer?
Misc.
100
If f(x) is continuous on a given interval [a, b], then...
1) lim x->a- f(x) = f(a)
2) lim x->a+ f(x) = f(a)
3) lim x->a f(x) = f(a)
100
DOUBLE JEOPARDY: The length s of each side of an equilateral triangle is increasing at a rate of 13 feet per hour. Find the rate of change of the area when s = 41 feet.
(533 sqrt 3)/2 ft^2/hr
100
Derivative of eu
eu * u'
100
The Integral of sin(x)dx is equal to -cos(x)
The Integral of sin(x)dx is -cos(x) + C
100
What fruit does raisins come from?
Grapes
200
If I wanted to prove the continuous f(x) has a minimum or maximum on [a, b], then I would use the _____ thorem
EVT
200
A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. Find the rate of change of the radius when r = 30 centimeters. (V = [4pi/3]*r3)
2/9pi cm/min
200
Derivative of |u|
u'/|u|
200
DOUBLE JEOPARDY:
1. Integral of ex/2dx from 0 to 2
2. 2[ex/2]20
3. 2e
3. 2e - 2e0 = 2e - 2
200
What's the smallest country in the world?
Vatican City
300
DOUBLE JEOPARDY: If a midpoint sum is used on a function which is concave up, then it is an ____estimation
Underestimation
300
A plane is flying directly away from you at 500 mph at an altitude of 3 miles. How fast is the plane's distance from you increasing at the moment when the plane is flying over a point on the ground 4 miles from you?
400 mph
300
Integral of sec(u)
ln|sec(u) + tan(u)| + C
300
Q: Find the position of Particle P at t=1 if the velocity of Particle P is given by v(t) = sin(t1.5) and Particle P is at position 5 at t=0.
1. Integral of v(t)dt from 0 to 1
2. Answer = 0.3706
1. 5 + Integral of v(t)dt from 0 to 1
2. Answer = 5.3706
300
When approaching a railroad crossing with no warning device in the US, the speed limit is ___ mph.
15 mph
400
What is the net change theorem?
The integral from a to b of f'(x) dx = f(b) - f(a)
400
A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and car B is driving east along the second road. At a particular time car A is 10 kilometers to the north of P and traveling at 80 km/hr, while car B is 15 kilometers to the east of P and traveling at 100 km/hr. How fast is the distance between the two cars changing?
127.6 km/h
400
DOUBLE JEOPARDY: Derivative of arcsec(u)
u'/(|u|*sqrt(u2-1))
400
Q: Find the region bounded by the area of y=sqrt(x), x=4, and y=0. Use shell method to find the volume of the solid generated by revolving the region about the y-axis.
1. V = pi * Integral of x(sqrt(x)) from 0 to 4
2. V = 64pi/5
1. V = 2pi * Integral of x(sqrt(x)) from 0 to 4
2. V = 128pi/5
400
There is a runaway trolley barreling down the railway tracks. Ahead, on the tracks, there are two people tied up and unable to move (Ella and Mindy). You can pull the lever to divert the trolley to a different set of tracks, but those tracks lead to a guaranteed 5 on the AP Calculus AB exam. You can only save one of the two options. Do you kill us or do you get a guaranteed 5 on the AP exam??
Obviously you save us.....
500
Describe the steps on how you would differentiate f(x) = Integral from h(x) to g(x) of f(t)dt using the Fundamental Theorem of Calculus
1. Split the limits of integrations as the integral of g(x) to 0 of f(t)dt + integral of 0 to h(x) of f(t)dt
2. Reverse the limits of integrations on the first integral and multiply by -1
3. Plug g(x) and h(x) in for t, then multiply by dg/dx and dh/dx, respectively.
500
The hands on a clock are of length 15mm (minute hand) and 12mm (hour hand). How fast is the distance between the tips of the hands changing at 3:00?
−17.1875 mm/h
500
What is the equivalence of cos(2u)?
cos2u - sin2u
1- 2sin2u
2cos2u - 1
500
Prove that the function f(x) = x-2 on [-1, 1] has some value where f'(c) is equal to 0.
1. f(x) is continuous on the closed interval and differentiable on the interval interval. Therefore, MVT applies.
2. f(-1) = 1, f(1) = 1
3. (1 - 1)/(1 - (-1))
4. 0/2 = 0
1. f(x) is NOT continuous on the closed interval [-1, 1]
500
1. Standard Jeopardy rules, but instead of players buzzing in to see if they can get the question the quickest, players will go in order and answer the question they chose.
2. If they get the question right, they will get the points. If they get it wrong, they will spin from a wheel of punishments later. They will not get the points deducted from their total, but other players can snipe the question by raising their board up first.
3. Each question will have a time limit of 15 seconds, but special questions will get an extended time limit.
4. There are special Double Jeopardy questions mixed in! You get double the points if you get it right, but also double the punishments if you get it wrong.
:D