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

Quadratic Formula
X = (-b ± sqrt(b² - 4ac))/(2a)

Degree/Radian Conversion Formulas
1 Radian = 180/p degrees
1 Degree = p/180 radians

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
Log_aN = log_bN / log_ba

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

Sum of an Arithmetic Sequence
S_n = n/2(A₁+A_n)

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

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

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

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

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

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)