Product rule and quotient rule
The derivative of x2 sin(x)
What is x2 cos(x) + 2x sin(x)
The value for x bar
What is -b/na
This is the indefinite integral of 5x4 - 2x + 7
What is x5 - x2 + 7x + C
find dy/dx for the equation x5 + y5 = 10xy2
What is (10y2 - 5x4) / (5y4 - 20xy)
given f(x) = (x - a)(x - b) ... (x - z), what is the constant term? It does not need to be simplified
What is 0
The derivative of (x + 1)(x2 - 3)
What is 2x(x + 1) + (x2 - 3)
This is what the x bar for a cubic function gives you
What is the inflection point
This is the indefinite integral of cos(x) + 1/sqrt(x)
What is sin(x) + 2sqrt(x) + C
This is dy/dx for x ln |y| + y ln|x| = pi
What is - (ln|y| + y/x) / (x/y + ln|x|)
S = 1 - 1 + 1 - 1 + 1...
Find S
What is 1/2
The derivative of (x2 + 1) / (x + 2)
What is [2x(x + 2) - (x2 + 1)]/(x + 2)2
given f(x) = (x + 1)/(x - 1)(x - 2), what is lim x -> 1 f(x)
What is DNE
This is the indefinite integral of (t2 + 1)(t - 3)
What is t4/4 - t3 + t2/2 - 3t + C
This is dy/dx for y2/x - x2/y = x + y
what is (x2y2 + y4 + 2x3y) / (2xy3 + x4 - x2y2)
Let K = 1 - 2 + 3 - 4 + 5 - 6...
Find K
What is 1/4
The derivative of xcos(x)(x2 + 1)
What is 2x(x cos x) - [xsin(x) + cos(x)](x2 + 1)
This is what we check for to see if we touch the x axis or cross it or if we jump the x axis or not for an asymptote
What is multiplicity
This is the indefinite integral of 2/x + sin(x)
What is 2ln|x| - cos(x) + C
This is d2y / dx2 for xy = 4
What is 8/x3
Let C = 1 + 2 + 3 + 4...
Find C
What is -1/12
The derivative of (x3 cos(x) + x2) / (x sin(x) + 1)
What is (x sin(x) + 1)(3x2cos(x) - x3 sin(x) + 2x) - (x3cos(x) + x2)(sin(x) + x cos(x)) / (x sin(x) + 1)2
given f(x) = (x + 1)(x + 2)2 / (x + 1)3 (x + 5), what is lim x -> -1 f(x)
What is infinity
This is the indefinite integral of (u3 - 4u2 + 6)/u2
What is u2 / 2 - 4u - 6/u + C
What is d2y/dx2 for x3 + y3 = 8
What is -16x/y5
You're in a square room. All the walls are mirrors. An assassin is trying to kill you with a lazer which bounces off the walls. Think of the lazer as a 1d line. You have blockers to save you. Every blocker has price $100. A blocker can block a single point within the room. Think of blockers, you and the assassin all as single points on a coordinate axis. If the lazer passes through a blocker, it disappears and you're safe. The blocker will absorb all the lazer's energy. However, if a lazer passes through you, you're dead. Find the minimum amount of money you need to spend to guarentee that you are alive.