Exercise · ZW-LIMIT-LAWS-001 · ★☆☆ Basic
Compute \(\lim_{x\to 2}\,\left(x^{2} + 3 x - 1\right)\).
Choose one option.
Show answer
- B. \(9\)
Explanation
The function is a polynomial or a rational function with a nonzero denominator at x = 2, so the limit is obtained by substituting x = 2: \(x^{2} + 3 x - 1\) evaluated at 2 gives \(9\).
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.
\[\lim_{x\to a}[f(x)\,g(x)]=\lim_{x\to a}f(x)\cdot\lim_{x\to a}g(x)\]
More practice problems: limit laws
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- ZW-LIMIT-LAWS-005 By the product law, what does lim _x→ a[f(x) g(x)] equal if both limits exist?
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- ZW-LIMIT-LAWS-009 When is it enough to substitute x=a to obtain the limit of a function?