Exercise · ZW-LIMIT-LAWS-003 · ★★☆ Intermediate
Compute \(\lim_{x\to 3}\,\frac{x^{2} + 1}{x - 1}\).
Choose one option.
Show answer
- D. \(5\)
Explanation
The function is a polynomial or a rational function with a nonzero denominator at x = 3, so the limit is obtained by substituting x = 3: \(\frac{x^{2} + 1}{x - 1}\) evaluated at 3 gives \(5\).
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-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-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?