Calculus for Life Sciences

ALGEBRA

Let P(x₁, y₁) and Q(x₂, y₂).

Distance between P and Q is .

Pythagorean theorem: If ΔABC is a right triangle with sides a and b, and hypotenuse c (the side opposite the right angle) then a² + b² = c².

Quadratic formula: If ax² + bx + c = 0, a ≠ 0, then x = .

Factoring rules: x² − y² = (x − y)(x + y) x³ − y³ = (x − y)(x² + xy + y²) x³ + y³ = (x + y)(x² − xy + y²)

Factorial: n! = n(n − 1)(n − 2)···3·2·1; 0! = 1; n! = n(n − 1)!

Binomial expansion: (a + b)² = a² + 2ab + b² (a + b)³ = a³ + 3a²b + 3ab² + b³ (a + b)ⁿ =

GEOMETRY

(A represents area, P represents perimeter, C represents circumference, V represents volume, S represents total surface area)

TRIGONOMETRY

Trigonometric functions Let θ be an angle in standard position with A = (a, b) the point of intersection of θ and the unit circle. Then the trigonometric functions are defined by:

PROBABILITY

The probability of an event E occurring ...