Bepalen van limieten door middel van directe substitutie

A moving motorist follows a smooth path, described by a position function that depends on time.

The goal is to determine the motorist’s position, modeled by a quadratic expression, as time approaches a specific value, such as 4 seconds.

This expression produces a position function that changes smoothly and predictably as time increases.

On a graph, the curve representing position bends upward, indicating that the rate at which position changes increases over time.

This behavior is described mathematically using a limit, which examines how the position behaves as time gets arbitrarily close to 4 seconds.

Since the function is continuous—without breaks or jumps—well-defined for all inputs, and both one-sided limits match, the limit can be evaluated directly by substitution.

Each term in the expression is computed by substituting the time value into the formula.

This produces a single numerical value representing the position at that time.

On the graph, this result corresponds to a point lying exactly on the curve at 4 seconds.

The value reflects the motorist’s position precisely—without estimation, rounding, or approximation.