SME
Calculus I · Problem type
Limits at infinity of a quotient
Use this for “Find the limit of (5x² − x) ÷ (2x² + 7) as x → ∞.”
Sort
Compare the highest powers on top and bottom.
Tap a card, then tap its group.
Assumptions
•
As x → ∞, only the highest power on top and on the bottom matters.
•
Divide the top and the bottom by the highest power of x on the bottom; every term with x below then → 0.
Topic check
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Related lessons
Limits and continuity
Main lesson
Make a piecewise function continuous
Use this for “Find k so that f(x) = 3x + k (x < 2), x² + 1 (x ≥ 2) is continuous.”
The intermediate value theorem
Use this for “Show that x³ + x − 1 = 0 has a root between 0 and 1.”
The limit of sin(kx) ÷ (mx)
Use this for “Find the limit of sin(3x) ÷ (2x) as x → 0” or “Find k so that sin(kx) ÷ (2x) → 3 as x → 0.”
Find δ for a given ε (a line)
Use this for “For lim (3x − 1) = 5 as x → 2, find δ when ε = 0.06.”
Kinds of discontinuity
Use this for “Is the discontinuity of (x² − 4) ÷ (x − 2) at x = 2 removable?”