Exercise · ZW-LIMIT-LAWS-005 · ★☆☆ Basic
By the product law, what does \(\lim_{x\to a}[f(x)\,g(x)]\) equal if both limits exist?
Choose one option.
Show answer
- B. \(\lim_{x\to a}f(x)\cdot\lim_{x\to a}g(x)\)
Explanation
The product law says the limit of a product is the product of the limits, provided both exist. Sum, difference and quotient correspond to other laws.
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-004 Compute lim _x→ 4 √x (x - 1).
- 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?