Limit Calculator

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What is a Limit?

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a particular value. The limit of f(x) as x approaches a, written as lim(x→a) f(x), is the value that f(x) gets arbitrarily close to as x gets arbitrarily close to a.

A limit describes the value that a function approaches as the input approaches a specific value. Use our free calculator to find limits instantly with step-by-step solutions. Simply enter any function like x^2, sin(x)/x, or (1+1/x)^x and get the limit with detailed explanations.

Key Facts About Limits

• •lim(x→0) sin(x)/x = 1 (fundamental trigonometric limit)
• •lim(x→∞) (1+1/x)^x = e (definition of Euler's number)
• •lim(x→0) (e^x-1)/x = 1
• •L'Hôpital's Rule: For 0/0 or ∞/∞, take derivatives of numerator and denominator
• •One-sided limits: x→a⁺ (from right) and x→a⁻ (from left)
• •A two-sided limit exists only if both one-sided limits exist and are equal
• •If direct substitution works, the function is continuous at that point
• •Limits at infinity describe end behavior of functions

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