Calculus Glossary

A function $F$ whose derivative equals $f$. Also called an indefinite integral.

A rule for differentiating composite functions: $\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$.

A function is continuous at a point if its limit equals its value at that point.

A sequence or series approaches a finite limit as more terms are added.

The signed area under a curve between two bounds: $\int_a^b f(x)\,dx$.

The instantaneous rate of change of a function, representing the slope of the tangent line.

An equation involving derivatives of an unknown function.

A sequence or series that does not approach a finite limit.

Maximum or minimum values of a function, either local or absolute.

The theorem linking differentiation and integration as inverse processes.

The general antiderivative of a function, written with $+ C$.

A point where the concavity of a function changes ($f''$ changes sign).

The process of finding the integral (antiderivative or area under curve) of a function.

A method for evaluating limits of indeterminate forms ($\frac{0}{0}$ or $\frac{\infty}{\infty}$) using derivatives.

The value a function approaches as its input approaches a given value.

An approximation of the integral using rectangles under the curve.

The sum of the terms of a sequence, either finite or infinite.

A representation of a function as an infinite sum of terms calculated from its derivatives at a point.