Continuous Functions

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:


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:

limit-discontinuity.png


Sources

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