12th grade Limits at infinity and end behavior worksheet

Limits at infinity and end behavior

Grade 12 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari compares the strongest terms of f(x) = (4x² − 1)/(2x³ + x). What happens as x → ∞?

   • f(x) → 2 as x → ∞
   • f(x) → +∞ as x → ∞
   • f(x) → 0 as x → ∞
2. 2.

   Esme compares the strongest terms of f(x) = (5x + 3)/(x² − 2). What happens as x → ∞?

   • f(x) → 5 as x → ∞
   • f(x) → 0 as x → ∞
   • f(x) → +∞ as x → ∞
3. 3.

   Jun compares the strongest terms of f(x) = (-2x⁴ + x)/(5x³ + 1). What happens as x → ∞?

   • f(x) → −∞ as x → ∞
   • f(x) → -2/5 as x → ∞
   • f(x) → 0 as x → ∞
4. 4.

   Kira looks at f(x) = (2x³ + 1)/(x² − 4) far to the left. What happens as x → −∞?

   • f(x) → 2 as x → −∞
   • f(x) → +∞ as x → −∞
   • f(x) → −∞ as x → −∞
5. 5.

   Milo looks at f(x) = (5x⁵ − 2)/(x⁴ + 1) far to the left. What happens as x → −∞?

   • f(x) → 5 as x → −∞
   • f(x) → +∞ as x → −∞
   • f(x) → −∞ as x → −∞
6. 6.

   Noah looks at f(x) = (-x³ + 7)/(2x² − 3) far to the left. What happens as x → −∞?

   • f(x) → -1/2 as x → −∞
   • f(x) → +∞ as x → −∞
   • f(x) → −∞ as x → −∞
7. 7.

   A tank's salt level is S(t) = 30t/(200 + 5t) after t minutes. Pia asks where it levels off. What is the limit as t → ∞, in g per liter?
8. 8.

   A club's app gains members: M(t) = 500t/(2t + 20) after t minutes. Ren asks where it levels off. What is the limit as t → ∞, in members?
9. 9.

   Sugar dissolves in a pitcher: C(t) = 12t/(50 + 4t) after t minutes. Tala asks where it levels off. What is the limit as t → ∞, in g per cup?
10. 10.

    A sunflower grows: h(t) = 90t/(15 + 2t) after t minutes. Zee asks where it levels off. What is the limit as t → ∞, in cm?