Exercise · ZW-CONTINUOUS-FUNCTION-001 · ★☆☆ Basic
Which of the following is NOT a condition for f to be continuous at a?
Choose one option.
Show answer
- A. That f is differentiable at a
Explanation
The three conditions for continuity are: f(a) is defined, the limit exists and the limit equals f(a). Differentiability is not a condition (for example, |x| is continuous at 0 but not differentiable there).
Review the concept: Continuous function
A function \(f\) is continuous at \(a\) if \(f(a)\) is defined, its limit as \(x\) tends to \(a\) exists and equals \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
More practice problems: continuous function
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