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A function is continuous at a number \(a\) if

\[ \lim_{x\ \to a }(f(x)) = f(a)\]

The above statement looks like just one thing must happe for a function to be continuous at \(a\), but to check if a function is continuous, we need three conditions satisfied:

- \(f(a)\) must be defined (\(a\) is in the domain of \(f\)).
- \(\lim_{x \to a}f(x)\) exists (the right and left limits must agree).
- \(\lim_{x \to a}f(x) = f(a)\).

Take a look at the picture below and try to determine if the function $f$ is continuous at \(x = 1,2,3\) and \(4\). If the functions is not continuous at one of the numbers, make a list of all of the above above conditions that the function does not satisfy.

The solution is discussed in the video below.

- Last Updated: Apr 19, 2023 1:48 PM
- URL: https://libraryguides.centennialcollege.ca/c.php?g=717032
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