Fraction Limit Calculator
Calculate the limit of a rational function (fraction) as x approaches any value. Understand limits step by step with our free tool.
Step 1: Define f(x) = (Ax + B) / (Cx + D)
Rational function limit
For linear/linear fractions, the limit as x→a is computed by substitution. If 0/0 occurs, the limit equals A/C (derivative ratio).
Step 2: Limit options
Classic limits
sin(x)/x → 1 (x→0) (1-cos(x))/x → 0 (eˣ-1)/x → 1
Limit Result
Limit of f(x) as x → 1.0
Classic Limits Comparison
| Limit expression | Value |
|---|
How the limit is computed
For f(x) = (Ax + B) / (Cx + D) as x → a
1. Substitute x = a into numerator and denominator.
2. If denominator ≠ 0, limit = (A·a + B) / (C·a + D).
3. If denominator = 0 and numerator ≠ 0, the limit is infinite (sign depends on direction).
4. If both are 0, we have an indeterminate 0/0. For linear numerator/denominator, the limit equals A / C (derivatives).
Example: (2x+2)/(x+1) as x→ -1 gives 0/0 → limit = 2/1 = 2.
Master limits with step‑by‑step help
Get a detailed explanation of your limit problem, including one‑sided limits and L’Hôpital’s rule.
Request Analysis