Calculus
Free lessons and practice worksheets for calculus — worked examples, common mistakes, and step-by-step solutions.
- 01Calculus3 min read
Differentiation
Differentiation is the mathematical process of finding the derivative of a function, which represents the instantaneous rate of change at any given point. The derivative of f(x) = 3x² is f'(x) = 6x, meaning at x = 2, the function changes at a rate of 12 units per unit input. This fundamental operation in calculus transforms polynomials, trigonometric functions, and exponentials into expressions that describe their slopes.
- 02Calculus3 min read
Integration
Integration is the mathematical process of finding the antiderivative of a function, essentially reversing differentiation. The power rule for integration states that ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, where C represents the constant of integration. Definite integrals evaluate between specific bounds and represent the area under a curve.
- 03Calculus3 min read
Limits
A limit describes the value that a function approaches as its input variable gets arbitrarily close to a specific number. Limits form the foundation of calculus by making precise the intuitive notion of "approaching" a value without necessarily reaching it. The formal definition uses epsilon-delta notation, but most elementary limit problems can be solved through direct substitution or algebraic manipulation.