Exercise · ZW-CONTINUOUS-FUNCTION-006 · ★★☆ Intermediate
Which value of k makes \(f(x)=\dfrac{x^{2}-9}{x-3}\) continuous at \(x = 3\) when \(x\neq3\) and \(f(3)=k\)?
Choose one option.
Show answer
- D. \(6\)
Explanation
For continuity, k must equal the limit: \(\lim_{x\to3}\dfrac{x^{2}-9}{x-3}=\lim_{x\to3}(x+3)=6\).
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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