Limit Calculator

Calculate limits of functions with step-by-step analysis

Function Type

Variable

Function f(x)

Approach Value

Direction

Limit Rules

Basic Properties

lim(f + g) = lim(f) + lim(g)

lim(f · g) = lim(f) · lim(g)

lim(f/g) = lim(f)/lim(g) if lim(g) ≠ 0

lim(c·f) = c·lim(f)

lim(f^n) = [lim(f)]^n

Standard Limits

lim(x→0) sin(x)/x = 1

lim(x→0) (1-cos(x))/x = 0

lim(x→∞) (1+1/x)^x = e

lim(x→0) (e^x - 1)/x = 1

lim(x→0) ln(1+x)/x = 1

Applications

Calculus

Definition of derivatives
Definition of integrals
Continuity analysis
Asymptote determination

Physics

Instantaneous velocity
Rate of change
Thermodynamic limits
Quantum mechanics

What is a Limit?

A limit describes the behavior of a function as its input approaches a particular value. It's fundamental to calculus and helps us understand continuity, derivatives, and integrals. The limit exists if the function approaches the same value from both directions.