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.

$\frac{Δy}{Δx} = \frac{y_2-y_1}{x_2-x_1}$

$\lim_{x\to a} f(x)$

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.