Compute one-sided and two-sided limits, including L’Hôpital’s rule.
A limit calculator evaluates one-sided and two-sided limits of functions, including limits at infinity and indeterminate forms (0/0, ∞/∞, 0·∞, ∞ − ∞, 0⁰, ∞⁰, 1^∞). Limits are the foundation of calculus — derivatives, integrals, and continuity are all defined via limits.
Most limits with indeterminate form are evaluated using L'Hôpital's rule, factoring/simplification, or known limit identities (e.g. lim sin(x)/x = 1 as x → 0).
\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)} \quad (\text{L'Hôpital})
Inputs: Evaluate lim (sin(x) − x) / x³ as x → 0
Three main cases: (1) one-sided limits disagree (the function jumps), (2) the function oscillates without settling (e.g. sin(1/x) as x → 0), or (3) the function grows unboundedly. Note that a limit of "+∞" or "−∞" is generally said to "not exist" in the strict sense but is "exist as an infinite limit" in a more relaxed convention.
If f(x) ≤ g(x) ≤ h(x) near a, and lim f = lim h = L, then lim g = L too. Used to evaluate limits that are hard to attack directly by squeezing the function between two simpler functions with known equal limits. Classic application: proving lim sin(x)/x = 1 as x → 0.
EMI Calculator Mortgage Calculator SIP Calculator Compound Interest GST / VAT Calculator Salary Calculator Unit Converter Currency Converter Scientific Calculator Concrete Calculator Paint Calculator Tile Calculator Calorie / TDEE Body Fat Macro Calculator O-Ring Sizes Bolt & Nut Sizes Pipe Sizes Wire Gauge AWG Needle Gauge Chart IV Cannula Sizes Suture Sizes Catheter French Sizes Drug Dosage See all 90+ calculators ›