Limit laws and direct substitution

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari knows lim f(x) = -2 as x → 1. What is the limit of [f(x)]^3 as x → 1?

   -8
2. 2.

   Bo knows lim f(x) = 3 as x → 4. What is the limit of [f(x)]^2 as x → 4?

   9
3. 3.

   Kira finds the limit of (x² + 5)/(x + 4) as x → -2. The bottom is not 0 there. What is the limit?

   9/2
4. 4.

   Luz finds the limit of (x² − 1)/(x + 2) as x → 3. The bottom is not 0 there. What is the limit?

   8/5
5. 5.

   Milo finds the limit of (x² + 9)/(x + 3) as x → -1. The bottom is not 0 there. What is the limit?

   5
6. 6.

   Noah finds the limit of (x² + 1)/(x + 7) as x → -3. The bottom is not 0 there. What is the limit?

   5/2
7. 7.

   A cup of coffee cools in a 20 °C room: T(t) = 20 + 60(1/2)^(t/10) °C after t minutes. Pia asks where T heads as t → 10. What is that limit, in °C?

   50
8. 8.

   A bowl of soup cools in a 22 °C room: T(t) = 22 + 72(1/2)^(t/8) °C after t minutes. Ren asks where T heads as t → 16. What is that limit, in °C?

   40
9. 9.

   A mug of cocoa cools in an 18 °C room: T(t) = 18 + 64(1/2)^(t/5) °C after t minutes. Tala asks where T heads as t → 10. What is that limit, in °C?

   34
10. 10.

    A pan of rice cools in a 25 °C kitchen: T(t) = 25 + 40(1/2)^(t/12) °C after t minutes. Zee asks where T heads as t → 12. What is that limit, in °C?

    45