Formulas:

Operations With Functions:

Sum: (f + g)(x) = f(x) + g(x)
Difference: (f - g)(x) = f(x) - g(x)
Product (f*g)(x) = f(x) * g(x)
Quotient (f/g)(x) = f(x) / g(x)

Composition of Functions:

[f*g] (x) = f(g(x))

Inverse Functions:
[f*g] (x) = [g * f] (x)

Distance Formual Between Two Points:
D = (x2 - x1 )2 + (y2 - y1 )2)1/2

X = (-b ± sqrt(b2 - 4ac))/(2a)

Length of an Arc:
S = rq

Linear and Angular Velocity
V = r * (q/t)

Area of a Circular Sector
A = 0.5r2q

Area of a Triangle
K = 0.5*b*c*sin(A)
K = 0.5*c2* sin(a)*sin(b)/sin(c)

Hero's Formula
K = (s(s-a)(s-b)(s-c))1/2

Area of a circular segment
S = 0.5r2(alpha - sin(alpha))

Distance from a Point to a Line
D = Ax1 + By1 + c / ± (a2 + b2)1/2

Conversion from Polar to Rectanglar Coordinates:
X = r*cos(theta)
Y = r*sin(theta)

Conversion from Rectangular to Polar
R = (x2 + y2)1/2
q = arctan (y/x) when x > 0
q = arctan(y/x) + PI when x <0

Length of a Segment Tanget to a Circle
T = ((x1 - h)2 + (y1 -k)2 - r2)1/2

Compound Interest Formulas
A = P(1 +r/n)(nt)
A = Pe(rt)

Change of Base Formula
LogaN = logbN / logba

Nth Term of an Arithmetic Sequence
An = A1 + (n-1)d

Sum of an Arithmetic Sequence
Sn = n/2(A1+An)

Nth Term of a Geometric Sequence
An = A1*R(n-1)

Sum of a Geometric Sequence
Sn = A1 - A1*Rn / 1-R

Sum of an Infinite Geometric Series
Sn = A1 / (1-R)

Euler's Formula
-e(l*alpha) = cos(alpha) + sqrt(-1) sin(ALPHA)

Verhulst Population Model
Pn-1 = Pn + R*pn(1-Pn)

Defininition of Permutation
P(n,n) = n!, P(n, r) = n!/(n-r)!

Definition of Combination
C(n, r) = n!/((n-r)!r!)

Limit of a Polynomial Function
Lim x->r P(x) = P(r)

Limit of a Trigonometric Function
Limit x->0 SIN(x)/x = 1

Power Formula
F(x) = cnx^(n-1)