Notation

Conventions used across this site (and common variants you may see elsewhere).

Functions

• $f(x)$: value of $f$ at $x$. Sometimes $y = f(x)$.
• Composition: $(f \circ g)(x) = f(g(x))$.
• Domain / range: $\operatorname{dom}(f)$, $\operatorname{ran}(f)$ when needed.

Limits and continuity

• Limit: $\displaystyle \lim_{x \to a} f(x)$. One-sided: $x \to a^+$, $x \to a^-$.
• Continuity at $a$: $\lim_{x \to a} f(x) = f(a)$ (three-part checklist: defined, limit exists, equal).

Derivatives

• Prime: $f'(x)$, $y'$. Operator: $\dfrac{d}{dx}$, $\dfrac{dy}{dx}$.
• Evaluation at $a$: $f'(a)$, $\left.\dfrac{dy}{dx}\right|_{x=a}$.

Integrals

• Antiderivative / indefinite: $\int f(x)\,dx$ (always include $dx$).
• Definite: $\displaystyle \int_a^b f(x)\,dx$.