Exercise · ZW-CONTINUOUS-FUNCTION-012 · ★☆☆ Basic
Let \(f(x)=\dfrac{x^2-4}{x-2}\) if \(x\ne2\) and \(f(2)=k\). For which \(k\) is it continuous at \(2\)?
Choose one option.
Show answer
- C. \(k=4\)
Explanation
For \(x\ne2\), \(f(x)=x+2\), whose limit at \(2\) is \(4\). Continuity requires \(f(2)=4\).
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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