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A Function $f(x)$ is continuous if the Limit of this function always exists otherwise the function is discontinuous

- $f(x)$ is continuous at $x = a$ if $\lim\limits_{x \to a} f(x) = f(a)$
- $f(x)$ is continuous everywhere if its continuous for all $a$ in the
**domain**of $f(x)$

Many functions are continuous, for example:

- Polynomial Functions
- Rational Functions
- Trigonometric Functions
- Exponential Functions and Logarithms

Careful!

- some functions might look discontinuous, but they may be continuous
- this is the case when the discontinuously-looking points are not in the domain
- but if the function is defined in this point, then it's discontinuous

Discontinuous: