Limit Calculator

What is a Limit?

The limit of f(x) as x approaches a value c is the value that f(x) gets closer and closer to.

lim (x→c) f(x) = L

Key Limit Rules:

• Direct substitution: If f(c) is defined and continuous, the limit equals f(c)
• Sum rule: lim [f(x) + g(x)] = lim f(x) + lim g(x)
• Product rule: lim [f(x) × g(x)] = lim f(x) × lim g(x)
• Quotient rule: lim [f(x)/g(x)] = lim f(x) / lim g(x) (if denominator ≠ 0)

Special Limits:

• lim (x→0) sin(x)/x = 1
• lim (x→∞) (1 + 1/x)^x = e ≈ 2.71828
• lim (x→0) (e^x - 1)/x = 1

One-sided limits:

• Left limit (x→c⁻): approaching from values less than c
• Right limit (x→c⁺): approaching from values greater than c