Exercise · ZW-LIMIT-LAWS-006 · ★☆☆ Basic
Besides the existence of the limits of numerator and denominator, what does the quotient law require?
Choose one option.
Show answer
- A. That the limit of the denominator be nonzero
Explanation
To divide limits, the limit of the denominator cannot be zero, since the quotient would be undefined. The law does not require the functions to be polynomials.
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-005 By the product law, what does lim _x→ a[f(x) g(x)] equal if both limits exist?
- 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?