L'Hospital's rule

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari rewrites x²(1 − cos(3/x)) as (1 − cos(3t))/t² with t = 1/x, then uses L'Hospital's rule. What is the limit as x → ∞?

   9/2
2. 2.

   Bo rewrites x²(1 − cos(5/x)) as (1 − cos(5t))/t² with t = 1/x, then uses L'Hospital's rule. What is the limit as x → ∞?

   25/2
3. 3.

   Esme rewrites x²(1 − cos(6/x)) as (1 − cos(6t))/t² with t = 1/x, then uses L'Hospital's rule. What is the limit as x → ∞?

   18
4. 4.

   Luz takes ln of y = (1 + 2/x)^(3x) and uses L'Hospital's rule as x → ∞. What is the limit of y, to the nearest hundredth?

   403.43
5. 5.

   Milo takes ln of y = (1 − 1/x)^(2x) and uses L'Hospital's rule as x → ∞. What is the limit of y, to the nearest hundredth?

   0.14
6. 6.

   Noah takes ln of y = (1 + 1/x)^(3x) and uses L'Hospital's rule as x → ∞. What is the limit of y, to the nearest hundredth?

   20.09
7. 7.

   Pia uses L'Hospital's rule twice on the limit of (1 − cos(2x))/(1 − cos(3x)) as x → 0. What is the limit?

   4/9
8. 8.

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

   16/9
9. 9.

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

   25/4
10. 10.

    Zee uses L'Hospital's rule twice on the limit of (1 − cos(6x))/(1 − cos(5x)) as x → 0. What is the limit?

    36/25