What would you like to understand?

At an interior point $a$, a function is continuous if it passes three tests: $f(a)$ is defined, the two-sided limit $\lim_{x\to a}f(x)$ exists, and this limit equals $f(a)$. The existence of the two-sided limit requires the left and right limits to agree.

Conditions: The point $a$ is an interior point of the function's domain.; The two-sided limit requires agreeing left and right limits.

At an interior point $a$, a function is continuous if it passes three tests: $f(a)$ is defined, the two-sided limit $\lim_{x\to a}f(x)$ exists, and this limit equals $f(a)$. The existence of the two-sided limit requires the left and right limits to agree.

Conditions: The point $a$ is an interior point of the function's domain.; The two-sided limit requires agreeing left and right limits.