MATH 01130 · Limits & continuity
Infinite limits / asymptotes
Definition
An infinite limit means |f(x)| grows without bound as x→a (vertical asymptote) or as x→±∞ (behavior at infinity). Horizontal asymptotes are finite limits as x→±∞.
Read this
Vertical asymptote at x=a often appears when the denominator → 0 while the numerator stays nonzero. Check one-sided signs.
For rationals as x→∞: compare degrees. deg(num)<deg(den) → HA y=0; equal → ratio of leading coeffs; num higher → no HA (oblique possible).
Infinite limits are not “equal to ∞” as a real number — we say the limit is ∞ (or −∞) as a description of unbounded growth.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
Click the card to flip
Try this
Attempt each problem first, then open the worked solution.
1.Find all asymptotes of (x+1)/(x−2).
2.Describe lim x→0⁺ 1/x and lim x→0⁻ 1/x.