Exercise · ZW-ONE-SIDED-LIMITS-008 · ★★★ Advanced
Let \(f(x)=x+1\) if \(x<2\) and \(f(x)=x^2-1\) if \(x\ge 2\). Compute \(\lim_{x\to 2} f(x)\).
Choose one option.
Show answer
- C. \(3\)
Explanation
From the left \(x+1\to 3\) and from the right \(x^2-1\to 3\). Since they agree, the limit is \(3\).
Review the concept: One-sided limits
The left-hand limit uses only values \(x<a\) and the right-hand limit only values \(x>a\). The limit of \(f\) at \(a\) exists if and only if both one-sided limits exist and are equal.
\[\lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)=L\]
More practice problems: one-sided limits
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