Exercise · ZW-LIMIT-LAWS-008 · ★★★ Advanced
Compute \(\lim_{x\to 1}\left[\frac{x^{2}-1}{x-1}+\frac{2}{x+1}\right]\).
Choose one option.
Show answer
- C. \(3\)
Explanation
For \(x\neq 1\), \(\frac{x^{2}-1}{x-1}=x+1\), whose limit is 2; the second term tends to \(\frac{2}{2}=1\). The sum of the limits is \(2+1=3\).
Review the concept: Limit laws
If \(\lim_{x\to a} f(x)\) and \(\lim_{x\to a} g(x)\) exist, the limit of their sum, difference, product or quotient (with nonzero denominator) is the same operation applied to the limits.
\[\lim_{x\to a}[f(x)\,g(x)]=\lim_{x\to a}f(x)\cdot\lim_{x\to a}g(x)\]
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