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Continuity of Functions

Continuity of Functions

Continuity at a Point via Formulas

It's good to have a feel for what continuity at a point looks like in pictures. However, sometimes we're asked about the continuity of a function for which we're given a formula, instead of a picture. When this happens, remember that the following three statements must all hold for f to be continuous at c.

  1. I. The function f is defined at x = c.
      
  2. The limit  exists.
      
  3. The value f(c) agrees with the limit 
      

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