Algebra
Solve for x:
2x + 3 = 9
x = 3
Evaluate:
sin(45)
sqrt(2)/2
What has to be broken to be used?
An egg
Find the limit as x approches 0:
sin(x)/x
limit = 1
Find the derivative of the vector valued function:
r(t) = <t2, sin(t), et>
r'(t) = <2t, cos(t), et>
x2 - 5x + 6
x = 2 and x = 3
Find the equation of the line that passes through the points (2,3) and (4,7).
y = 2x - 1
What is it that no one wants, but no one wants to lose?
A lawsuit
(2x + 1)dx
12
Find the integral of the vector valued function with the initial condition <1,2,1>:
r(t) = <2t, cos(t), et>
r'(t) = <t2 + 1, sin(t) + 2, et + 1>
Divide 2x3 - 3x2 + 4x - 5 by x - 2
2x2 + x + 2 + 3/x-2
Simplify the complex number:
(3 + 2i)(4 - 5i)
22 - 7i
A barrel of water weighed 60 pounds. Someone put something in it and now it weighs 40 pounds. What did the person add?
A hole
Use implicit differentiation to find dy/dx:
x2 + xy + y2 = 7
dy/dx = (-2x-y)/(x+2y)
Solve the integral using integration by parts:
(xex)dx
xex - ex + C
Common ratio: 2
Find the domain:
f(x) = sqrt(5-x)
x is less than or equal to 5
A man pushes his car up to the hotel and tells the owner that he is bankrupt. Why?
Because he’s playing Monopoly.
Find the derivative:
f(x) = e2xsin(x)
f'(x) = 2e2xsin(x) + e2xcos(x)
Find the arc length of the curve given the parametric equations x = 3t2 and y = 2t3 from t = 0 to t = 1.
7sqrt(14) - 4
Solve for x:
log2(x-1) + log2(x+1) = 3
x = 3
Extraneous: x = -3
Determine the polar coordinates of the point with Cartesian coordinates (-4, 4/sqrt(3)) where r is positive and 0 ≤ θ < 2pi.
(8, 2pi/3)
A troll has taken your brother and sister hostage. He will release your brother if you say something false. He will release your sister if you say something true. You can only give one statement. (It cannot be inherently paradoxical like saying “this statement is false”)
You will free my brother.
Determine the area of the region bounded by y = x2 and y = 4x - x2.
Evaluate the improper integral with bounds from 1 to infinity:
(ln(x)/x2)dx
-1