One-sided limits and existence of limit for JEE

Formula

\[\lim_{x\to a}f(x)\text{ exists }\iff \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)\]

Variables: Left-hand limit \(x\to a^-\), right-hand limit \(x\to a^+\).

Conditions: Both one-sided limits must be finite and equal for finite two-sided limit.

Piecewise functions and continuity/discontinuity at junction points.