L'Hospital's rule

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari sees 0/0 in the limit of (x³ − 8)/(x − 2) as x → 2, and uses L'Hospital's rule. What is the limit?

   12
2. 2.

   Bo sees 0/0 in the limit of (x⁴ − 81)/(x − 3) as x → 3, and uses L'Hospital's rule. What is the limit?

   108
3. 3.

   Jun sees 0/0 in the limit of (x⁴ − 16)/(x − 2) as x → 2, and uses L'Hospital's rule. What is the limit?

   32
4. 4.

   Kira uses L'Hospital's rule on the limit of sin(3x)/(2x) as x → 0. What is the limit?

   3/2
5. 5.

   Luz uses L'Hospital's rule on the limit of sin(5x)/(4x) as x → 0. What is the limit?

   5/4
6. 6.

   Milo uses L'Hospital's rule on the limit of sin(6x)/(5x) as x → 0. What is the limit?

   6/5
7. 7.

   Noah uses L'Hospital's rule on the limit of sin(2x)/(7x) as x → 0. What is the limit?

   2/7
8. 8.

   Ren uses L'Hospital's rule on the limit of (e^(5x) − 1)/(3x) as x → 0. What is the limit?

   5/3
9. 9.

   Tala uses L'Hospital's rule on the limit of (e^(6x) − 1)/(4x) as x → 0. What is the limit?

   3/2
10. 10.

    Zee uses L'Hospital's rule on the limit of (e^(8x) − 1)/(3x) as x → 0. What is the limit?

    8/3