Limits & Continuity · Definitions
Left-Hand Limit
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.
- 0 variables
- 2 worked examples
- 18 in Limits & Continuity
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
1 more worked examplePremium
Find lim(x→2⁻) floor(x).
Step-by-step solution locked.
Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
Related formulas
See all 18 Limits & Continuity formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Practice
Quiz yourself on Limits & Continuity
Left-Hand Limit is one of 18 Limits & Continuity formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.