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## Homework Statement

How would I demonstrate that a function is continuous? Would I just show that it's derivative exists? Thanks for the help.

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- Thread starter armolinasf
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How would I demonstrate that a function is continuous? Would I just show that it's derivative exists? Thanks for the help.

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Mark44

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But what if the function is not differentiable? There are functions that are not differentiable at a given point that happen to be continuous there. For example, y = |x| at x = 0.## Homework Statement

How would I demonstrate that a function is continuous? Would I just show that it's derivative exists? Thanks for the help.

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Then it would be where it's undefined? Also, would I have to examine its end behavior?

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Mark44

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No. My example function, f(x) = |x|, is defined everywhere.

How is continuity defined in your book?

How is continuity defined in your book?

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- #6

Mark44

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A function f is continuous at a number a in its domain iff

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

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