Continuity is a fundamental concept in calculus that describes the behavior of functions. Here, we'll explore some key properties:
- Property 1: If a function is continuous at a point, small changes in the input result in small changes in the output.
- Property 2: Polynomial functions are continuous everywhere.
- Property 3: The composition of continuous functions is continuous.
- Property 4: A function is continuous on an interval if it is continuous at every point in the interval.
Why Continuity Matters
Understanding continuity helps in calculating limits and in understanding the behavior of functions. It's foundational for tackling more complex calculus problems.