Limits at infinity and end behavior

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari wants the limit of √(9x² + 1)/(2x + 3) as x → ∞. What is it?

   3/2
2. 2.

   Bo wants the limit of √(16x² + 1)/(3x + 1) as x → ∞. What is it?

   4/3
3. 3.

   Esme wants the limit of √(25x² + 1)/(4x − 7) as x → ∞. What is it?

   5/4
4. 4.

   A hot drink cools as T(t) = 20 + 60e^(−0.1t) °C after t minutes. Kira asks where T heads in the long run. What is the limit as t → ∞?

   20
5. 5.

   A hot drink cools as T(t) = 22 + 70e^(−0.05t) °C after t minutes. Luz asks where T heads in the long run. What is the limit as t → ∞?

   22
6. 6.

   A hot drink cools as T(t) = 18 + 50e^(−0.2t) °C after t minutes. Milo asks where T heads in the long run. What is the limit as t → ∞?

   18
7. 7.

   Making club T-shirts costs $200 to set up plus $6 each, so the average cost is A(n) = (200 + 6n)/n dollars. Pia asks about huge orders. What is the limit as n → ∞?

   $6
8. 8.

   Making class mugs costs $150 to set up plus $4 each, so the average cost is A(n) = (150 + 4n)/n dollars. Ren asks about huge orders. What is the limit as n → ∞?

   $4
9. 9.

   Making team posters costs $90 to set up plus $3 each, so the average cost is A(n) = (90 + 3n)/n dollars. Tala asks about huge orders. What is the limit as n → ∞?

   $3
10. 10.

    Making school caps costs $120 to set up plus $5 each, so the average cost is A(n) = (120 + 5n)/n dollars. Zee asks about huge orders. What is the limit as n → ∞?

    $5