Function

How to prove that function is continuous

How to prove that function is continuous

Your pre-calculus teacher will tell you that three things have to be true for a function to be continuous at some value c in its domain:

  1. f(c) must be defined. ...
  2. The limit of the function as x approaches the value c must exist. ...
  3. The function's value at c and the limit as x approaches c must be the same.

  1. How do you show that a function is continuous?
  2. How do you prove a function is continuous example?

How do you show that a function is continuous?

Saying a function f is continuous when x=c is the same as saying that the function's two-side limit at x=c exists and is equal to f(c).

How do you prove a function is continuous example?

To prove that f is continuous at 0, we note that if 0 ≤ x<δ where δ = ϵ2 > 0, then |f(x) − f(0)| = √ x < ϵ. f(x) = ( 1/x if x ̸= 0, 0 if x = 0, is not continuous at 0 since limx→0 f(x) does not exist (see Example 2.7).

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