Exercise · ZW-LIMIT-LAWS-004 · ★★☆ Intermediate
Compute \(\lim_{x\to 4}\,\sqrt{x} \left(x - 1\right)\).
Choose one option.
Show answer
- C. \(6\)
Explanation
The function is a polynomial or a rational function with a nonzero denominator at x = 4, so the limit is obtained by substituting x = 4: \(\sqrt{x} \left(x - 1\right)\) evaluated at 4 gives \(6\).
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
- ZW-LIMIT-LAWS-001 Compute lim _x→ 2 (x^2 + 3 x - 1).
- ZW-LIMIT-LAWS-002 Compute lim _x→ 4 (x - 3) (x + 1).
- ZW-LIMIT-LAWS-003 Compute lim _x→ 3 (x^2 + 1)/(x - 1).
- ZW-LIMIT-LAWS-005 By the product law, what does lim _x→ a[f(x) g(x)] equal if both limits exist?
- ZW-LIMIT-LAWS-006 Besides the existence of the limits of numerator and denominator, what does the quotient law requir…
- ZW-LIMIT-LAWS-007 Compute lim _x→ 2 (x^2-4)/(x-2).
- ZW-LIMIT-LAWS-008 Compute lim _x→ 1[(x^2-1)/(x-1)+(2)/(x+1)].
- ZW-LIMIT-LAWS-009 When is it enough to substitute x=a to obtain the limit of a function?