Evaluate mathematical limits quickly and easily. Enter a function and the point it approaches to get a clear limit result with formulas, examples, and explanations.
Enter a function and the value x approaches.
A limit describes the value that a function approaches as its input gets closer to a particular number.
This means that as x gets closer and closer to a, the value of f(x) approaches L.
The limit of a sum equals the sum of the individual limits.
The limit of a product equals the product of the limits when the required limits exist.
The quotient rule can be used when the denominator limit is not zero.
lim sin(x)/x = 1 as x approaches 0.
Some functions grow without bound as x approaches a specific value.
Left-hand and right-hand limits can be different at discontinuities.
The calculator evaluates a function near the selected value of x. It samples values increasingly close to the point and uses mathematical limit rules to identify the value the function approaches.
Type a mathematical expression such as x², sin(x)/x, or a rational function.
Enter the value that x approaches, such as 0, 1, or 2.
Click Calculate Limit to see the estimated limit and supporting information.
Here are some common examples of limits used in calculus.
A limit is one of the most important concepts in calculus. It describes the value that a function approaches as its input gets arbitrarily close to a particular number.
Limits are used to define continuity, derivatives, integrals, instantaneous rates of change, and many other concepts in mathematics.
Limits allow mathematicians to study functions even when the function is undefined at a specific point. They are especially useful for analyzing discontinuities and understanding behavior near a particular value.
The derivative of a function is defined using a limit. It measures the instantaneous rate of change of a function at a particular point.