Limits that need factoring or rationalizing

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari wants the limit of (√(x + 5) − 3)/(x − 4) as x → 4. Direct substitution fails. What is the limit?

   1/6
2. 2.

   Bo wants the limit of (√(x + 12) − 4)/(x − 4) as x → 4. Direct substitution fails. What is the limit?

   1/8
3. 3.

   Esme wants the limit of (√(x − 3) − 2)/(x − 7) as x → 7. Direct substitution fails. What is the limit?

   1/4
4. 4.

   Jun wants the limit of (√(x + 21) − 5)/(x − 4) as x → 4. Direct substitution fails. What is the limit?

   1/10
5. 5.

   Kira wants the limit of (x³ − 64)/(x − 4) as x → 4. Direct substitution fails. What is the limit?

   48
6. 6.

   Milo wants the limit of (x³ − 216)/(x − 6) as x → 6. Direct substitution fails. What is the limit?

   108
7. 7.

   Noah wants the limit of (x³ + 64)/(x + 4) as x → -4. Direct substitution fails. What is the limit?

   48
8. 8.

   Pia wants the limit of (1/x − 1/2)/(x − 2) as x → 2. Direct substitution fails. What is the limit?

   -1/4
9. 9.

   Ren wants the limit of (1/x − 1/3)/(x − 3) as x → 3. Direct substitution fails. What is the limit?

   -1/9
10. 10.

    Tala wants the limit of (1/x − 1/4)/(x − 4) as x → 4. Direct substitution fails. What is the limit?

    -1/16