Showing that a function is continuous

  • Thread starter armolinasf
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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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  • #2
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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.
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.
 
  • #3
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Then it would be where it's undefined? Also, would I have to examine its end behavior?
 
  • #4
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No. My example function, f(x) = |x|, is defined everywhere.

How is continuity defined in your book?
 
  • #5
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It's defined by saying that a function is continuous if its graph is an unbroken curve over an interval
 
  • #6
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The way continuity at a point is usually defined is as a limit:
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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