Embedded Files
Quadratic roots
f(x) = ax^2 + bx + c
roots = (-b ± sqr(b^2-4ac)) / 2a
Combinations
nCr = n! / ( (n-r)! r! )
Derivatives
sin x cos x
cos x - sin x
tan x sec^2 x
Integrals
x^a x^(a+1) / (a+1), a>1
1/x ln |x|
e^x e^x
a^x a^x / (ln a)
tan x ln |(sec x)|
Simpson's rule
a?b f(x) dx ~=
1/3 . h(y0 + 4y1 + y2)
where, h = 1/2 . (b - a)
Trigonometry/Triangles
sin (A/2) = sqr((s-b)(s-c) / bc)
cos (A/2) = sqr( s(s-a) / bc )
- sine rule
a/(sin A) = b/(sin B) = c/(sin C) = 2R
- cosine rule
a^2 = b^2 + c^2 - 2bc . cos A
- circumcircle
R = abc / 4 . (area of triangle)
Single variable statistics
(number n, mean m) (E sigma, samp x)
derivation, dx = x - m
mean derivation = 1/n . E |dx|
E dx^2 = E x^2 - ((E x)^2) / n
variance = 1/n . E dx^2
standard deviation = sqr(var)
Double variable statistics
correlation coeff =
E (dx dy)/sqr((E dx^2)(E dy^2))
linear regression, y=a+bx
b = E (dx dy) / (E dx^2)
a = (mean y) - b (mean x)
Normal distribution
(mean m, variance s^2)
f(x) = 1/( s . sqr(2 pi) )
exp( -(x-m)^2 / (2s^2) )
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