Limit laws and direct substitution

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari knows lim f(x) = 4 and lim g(x) = -2 as x → 1. What is the limit of 3f(x) − g(x) as x → 1?

   14
2. 2.

   Esme knows lim f(x) = -1 and lim g(x) = -6 as x → 0. What is the limit of 4f(x) − 2g(x) as x → 0?

   8
3. 3.

   Jun knows lim f(x) = 7 and lim g(x) = -1 as x → 3. What is the limit of 2f(x) − 5g(x) as x → 3?

   19
4. 4.

   Kira finds the limit of x² + 3x − 1 as x → -2. A polynomial is smooth, so substitution works. What is the limit?

   -3
5. 5.

   Luz finds the limit of x² − 2x + 4 as x → -3. A polynomial is smooth, so substitution works. What is the limit?

   19
6. 6.

   Milo finds the limit of x² + 5x + 2 as x → -1. A polynomial is smooth, so substitution works. What is the limit?

   -2
7. 7.

   Noah finds the limit of x² + 1x + 6 as x → -4. A polynomial is smooth, so substitution works. What is the limit?

   18
8. 8.

   Pia finds the limit of √(x + 16) as x → 9. The root law says the limit goes inside. What is the limit?

   5
9. 9.

   Ren finds the limit of √(x + 64) as x → 36. The root law says the limit goes inside. What is the limit?

   10
10. 10.

    Zee finds the limit of √(x + 8) as x → 1. The root law says the limit goes inside. What is the limit?

    3