Limits that need factoring or rationalizing

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari wants the limit of (x² + 3x − 10)/(x − 2) as x → 2. Direct substitution fails. What is the limit?

   7
2. 2.

   Bo wants the limit of (x² + 2x − 15)/(x − 3) as x → 3. Direct substitution fails. What is the limit?

   8
3. 3.

   Esme wants the limit of (x² − 2x − 15)/(x + 3) as x → -3. Direct substitution fails. What is the limit?

   -8
4. 4.

   Jun wants the limit of (x² − 7x + 10)/(x − 2) as x → 2. Direct substitution fails. What is the limit?

   -3
5. 5.

   After multiplying by the conjugate, Luz's limit as x → 0 became 1/(√(x + 9) + 3). What is the limit?

   1/6
6. 6.

   After multiplying by the conjugate, Milo's limit as x → 9 became 1/(√(x + 7) + 4). What is the limit?

   1/8
7. 7.

   After multiplying by the conjugate, Noah's limit as x → 9 became 1/(√(x + 16) + 5). What is the limit?

   1/10
8. 8.

   Pia has the factored form (x − 3)(x + 2)/((x − 3)(x + 4)). What is its limit as x → 3?

   5/7
9. 9.

   Ren has the factored form (x + 2)(x + 5)/((x + 2)(x + 4)). What is its limit as x → -2?

   3/2
10. 10.

    Zee has the factored form (x − 4)(x − 1)/((x − 4)(x + 2)). What is its limit as x → 4?

    1/2