Limit Calculator
Solve limit problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations. Free to use with no signup required.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
lim x→a f(x) ≈ evaluate f(a ± ε) for decreasing ε: 0.1, 0.01, 0.001, 0.0001, ...
Numerical limit estimation evaluates f(x) at points increasingly close to a from both sides. If left and right limits agree, the two-sided limit exists. Useful for indeterminate forms like 0/0, ∞/∞.
Worked Examples
Example 1: lim sin(x)/x as x→0
Problem:f(x) = sin(x)/x, approach 0
Solution:Right: 0.9999998..., Left: 0.9999998... → Limit = 1
Result:Limit ≈ 1.00000000
Example 2: Removable discontinuity: (x²-1)/(x-1) as x→1
Problem:f(x) = (x*x-1)/(x-1), approach 1 (function is undefined exactly at x=1)
Solution:Simplifies algebraically to x+1 for all x≠1, so the limit as x→1 is 1+1 = 2, even though f(1) itself is undefined.
Result:Limit ≈ 2.00000000
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy