UNIT 5: Calculus

Formulae (SL & HL)

Limits

Limit Formula

Power Rule (Differentiation)

Chain Rule (Differentiation)

Product Rule (Differentiation)

Quotient Rule (Differentiation)

Standard Derivatives of Functions

Local Maximums (Differentiation)

Local Minimums (Differentiation)

Continuity (Differentiation)

• Continuity - A Function is continuous if:

  • f(x) is defined at every point in a domain.

  • There is a limit at every point.

  • The limit at a point is equal to the functional value at that point.

L’Hopital’s Rule

Implicit Differentiation

For any function with more than one variable, consider the variable that is not differentiated with respect to a function.

Notation of Indefinite Integrals

Integrals without fixed upper and lower boundaries for the integral (add constant of integration ‘c’).

Power Rule (Integration)

Integration by Substitution

Trigonometric Substitutions (Integration)

Standard Integrals of Functions

Fundamental Theorem of Calculus

Definite Integrals

Integrals with fixed upper and lower boundaries (constant of integration ‘c’ disappears).

Area between two Curves (Integration)

Integration by Parts

Tips for Integration by Parts

Volume of Revolutions (Integration)

Kinematics (Integration)

Separation of Variables (Integration)

Standard Logistic Equation (Integration)