Exercise · ZW-CONTINUOUS-FUNCTION-018 · ★★☆ Intermediate
Let \(f(x)=x\sin(1/x)\) for \(x\ne0\) and \(f(0)=k\). For which \(k\) is it continuous at \(0\)?
Choose one option.
Show answer
- B. \(k=0\)
Explanation
Since \(|x\sin(1/x)|\le|x|\), the limit at \(0\) is \(0\). We must set \(f(0)=0\).
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 \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
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