L'Hospital's rule

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari uses L'Hospital's rule twice on the limit of (1 − cos(3x))/(4x²) as x → 0. What is the limit?

   9/8
2. 2.

   Bo uses L'Hospital's rule twice on the limit of (1 − cos(4x))/(3x²) as x → 0. What is the limit?

   8/3
3. 3.

   Esme uses L'Hospital's rule twice on the limit of (1 − cos(5x))/(2x²) as x → 0. What is the limit?

   25/4
4. 4.

   Kira uses L'Hospital's rule on the limit of (e^(5x) − e^(-2x))/(3x) as x → 0. What is the limit?

   7/3
5. 5.

   Luz uses L'Hospital's rule on the limit of (e^(4x) − e^(-3x))/(14x) as x → 0. What is the limit?

   1/2
6. 6.

   Milo uses L'Hospital's rule on the limit of (e^(6x) − e^(2x))/(3x) as x → 0. What is the limit?

   4/3
7. 7.

   Pia uses L'Hospital's rule on the limit of (√(9 + 6x) − 3)/x as x → 0. What is the limit?

   1
8. 8.

   Ren uses L'Hospital's rule on the limit of (√(16 + 4x) − 4)/x as x → 0. What is the limit?

   1/2
9. 9.

   Tala uses L'Hospital's rule on the limit of (√(25 + 20x) − 5)/x as x → 0. What is the limit?

   2
10. 10.

    Zee uses L'Hospital's rule on the limit of (√(36 + 3x) − 6)/x as x → 0. What is the limit?

    1/4