Limit Calculator
Calculate limits of polynomial and rational functions as x approaches a finite value or ±∞. Shows algebraic solution, L'Hôpital's Rule when needed, and a numerical approach table.
| x (from left) | f(x) | x (from right) | f(x) |
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L'Hôpital's Rule
If lim f(x)/g(x) is 0/0 or ∞/∞, then:
Frequently Asked Questions
A limit describes the value a function approaches as the input approaches some value. Written as lim[x→c] f(x) = L, it means f(x) gets arbitrarily close to L as x gets close to c.
Indeterminate forms like 0/0, ∞/∞, 0×∞, ∞−∞, 0⁰, 1^∞, and ∞⁰ are limits that cannot be evaluated by direct substitution. They require algebraic manipulation or L'Hôpital's Rule.
If a limit produces 0/0 or ∞/∞, differentiate the numerator and denominator separately and take the limit of that ratio. Repeat if needed. Named after the French mathematician Guillaume de l'Hôpital (1661–1704).
lim[x→∞] f(x) = L means f(x) approaches L as x grows without bound. For rational functions, divide numerator and denominator by the highest power of x. The limit depends on the degrees of the polynomials.
Yes. The limit at c considers values near c, not at c. For example, lim[x→0] sin(x)/x = 1, even though the function is undefined at x=0 (0/0 form resolved by L'Hôpital or squeeze theorem).
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