Evaluating Limits by Direct Substitution

In the analysis of functions that represent continuous physical phenomena, it is often necessary to determine the output value as the input approaches a specific point. When a combination of algebraic terms defines the function and exhibits no discontinuities or abrupt changes near the point of interest, the limit of the function can be evaluate...

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 increas...