Math History
Name this formula: a2 + b2 = c2
Pythagorean Theorem
State L'Hopital's Rule
If indeterminate:
lim x -> c f(x) / g(x) = lim x -> c f'(x) / g'(x)
Name a trigonometric pythagorean identity.
e.g. in the form of (a2 + b2 = c2)
Varies
Name the formula for the area of a cone
1/3 * pi * r^2 * h
What is the formula for the sum of the angles in a n-side polygon
Who discovered the number 0
Aryabhata
Name an approximation technique for calculating definite integrals.
Varies on answer choice
Name the double angle formula for cos(x)
cos^2 (x) - sin^2(x)
System of Equations:
1. 5x + 8y = 67
2. 2x - y = 31
x = 15, y = -1
Name the first 10 digits of pi
3.141592653...
What is the name of this theorem: an + bn = cn , for n > 2
Fermat's Last Theorem
Name one of the parts of the Fundamental Theorem of Calculus
1. F'(x) = f(x)
2. Integral from bounds a to b of f(x) = F(b) - F(a)
Name the domains of arcsin() & arctan()
arcsin(): [-1,1]
arctan(): (- infinity , infinity)
2^x + 4(2^-x) = 5
x = 0
Four of the following: 0/0 , infinity / infinity , 0 * infinity , 0 ^ 0 , infinity ^ 0, 1 ^ infinity , infinity - infinity
The _____ Hypothesis is a hypothesis about the distribution of prime numbers
Riemann
Name the shape that has infinite surface area, but finite volume
Gabriel's Horn
Prove the half angle formula for sin(x)
Answer varies
Find the roots of: 6x3 + 7x2 - 37x - 42
x =-2, -3/2 , 7/3
Prove sqrt(2) is irrational
Varies
Who proved the Basel problem?
Euler
State the technique: Integration by parts
integral of u dv = u*v - integral of v * du
Prove how e^(i*pi) = -1
Answer varies
Find f(5):
f(0) = 1
f(1) = 2
f(n) = f(n-1) * f(n-2) + 1
What does this equate to:
x - (x3/3!) + (x5/5!) - (x7/7!) + (x9/9!)
sin(x)