The value that a function approaches as the input approaches some value.

The rate of change of a function at a specific point, found using limits.

A line that intersects a curve at two or more points.

A line that touches a curve at only one point, representing the instantaneous rate of change.

The slope of the secant line between two points on a curve.

Limits describe the behavior of a function as the input approaches a specific value. They are fundamental to calculus.

It's the rate of change at a single point, found by taking the limit of the average rate of change as the interval approaches zero.

Limits allow us to analyze function behavior at points where the standard rate of change formula would be undefined.

As the distance between two points on a curve approaches zero, the secant line approaches the tangent line.

The derivative of a function at a point is defined as the limit of the difference quotient as the change in x approaches zero.

Examine the graph of the function as x approaches the specified value from both sides. If the y-value approaches the same value from both sides, that is the limit.

Try direct substitution first. If it results in an indeterminate form (e.g., 0/0), try factoring, rationalizing, or other algebraic manipulations to simplify the expression before evaluating the limit.

Use algebraic techniques like factoring, rationalizing, or L'Hôpital's Rule (if applicable) to simplify the expression before evaluating the limit.