Limits & Continuity · Definitions

Right-Hand Limit

\lim_{x \to a^+} f(x) = L

The limit of f(x) as x approaches a from the right (from values greater than a). A two-sided limit exists if and only if both one-sided limits exist and are equal.

Conditions. f(x) must be defined on an open interval (a, d) for some d > a.

Worked examples

Find lim(x→0⁺) |x|/x.

For x > 0, |x| = x
So |x|/x = x/x = 1

Answer: lim(x→0⁺) |x|/x = 1

Find lim(x→0⁺) √x.

As x → 0 from the right, √x → √0 = 0

Answer: lim(x→0⁺) √x = 0

Related formulas

Left-Hand Limit Limit Definition (Epsilon-Delta)

Practice this and 135 more formulas in the CalcRef workspace — quizzes, reference tables, a 16-category unit converter, and an expression evaluator.