Limit definition
MathDefinition
The limit of a function f(x) as x approaches a value c is the value that f(x) gets closer and closer to as x gets closer and closer to c. The limit may exist even if f(c) is undefined. This concept is the foundation of calculus.
Examples
- lim(x→2) of (x²−4)/(x−2) = 4, even though the function is undefined at x = 2
- lim(x→0) of sin(x)/x = 1
- The speed of a car at an exact instant is defined as a limit of average speeds
Key Fact
lim(x→c) f(x) = L means f(x) can be made arbitrarily close to L by taking x sufficiently close to c.
Study This Concept
Practice limit definition with free review games in these units: