Exercise · ZW-CONTINUOUS-FUNCTION-007 · ★★☆ Intermediate
Which value of k makes continuous at \(x = 1\) the function defined by \(f(x)=x+k\) if \(x<1\) and \(f(x)=2x^{2}\) if \(x\geq1\)?
Choose one option.
Show answer
- C. \(1\)
Explanation
Both one-sided limits must agree: \(1+k=2\cdot1^{2}=2\), so k = 1.
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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