Derivatives for cbse — Continuity and Differentiability + 5 more topics

A function $f(x)$ is continuous at a point $x=a$ if three conditions are met:
1. $f(a)$ exists: The function is defined at that point.
2. $\lim_{x \to a} f(x)$ exists: As you approach $a$ from both the left and right sides, the function values approach the same number. This is called the limit.
3. $\lim_{x \to a} f(x) = f(a)$: The limit you found is exactly equal to the function's value at that point.