CalcRef

Limits & Continuity · Definitions

Left-Hand Limit

lim⁡x→a−f(x)=L\lim_{x \to a^-} f(x) = L

The limit of f(x) as x approaches a from the left (from values less than a).

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

Worked examples

Find lim(x→0⁻) |x|/x.
  1. For x < 0, |x| = -x
  2. So |x|/x = -x/x = -1

Answer: lim(x→0⁻) |x|/x = -1

Find lim(x→2⁻) floor(x).
  1. For x slightly less than 2 (e.g., 1.9, 1.99), floor(x) = 1

Answer: lim(x→2⁻) floor(x) = 1

Related formulas

Right-Hand LimitLimit Definition (Epsilon-Delta)

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