Limits with absolute value and trig

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari wants the limit of sin(5x)/sin(2x) as x → 0. What is it?

   5/2
2. 2.

   Esme wants the limit of sin(8x)/sin(5x) as x → 0. What is it?

   8/5
3. 3.

   Jun wants the limit of sin(4x)/sin(9x) as x → 0. What is it?

   4/9
4. 4.

   Kira uses the cosine limit near zero. What is the limit of (1 − cos(8x))/x² as x → 0?

   32
5. 5.

   Luz uses the cosine limit near zero. What is the limit of (1 − cos(10x))/x² as x → 0?

   50
6. 6.

   Milo uses the cosine limit near zero. What is the limit of (1 − cos(6x))/x² as x → 0?

   18
7. 7.

   Noah uses the cosine limit near zero. What is the limit of (1 − cos(3x))/x² as x → 0?

   9/2
8. 8.

   Pia studies 9|x − 2|/(x − 2) near x = 2. What is its limit as x → 2?

   • does not exist
   • 0
   • 9
9. 9.

   Tala studies 2|x − 4|²/(x − 4) near x = 4. What is its limit as x → 4?

   • does not exist
   • 0
   • 2
10. 10.

    Zee studies 7|x − 1|²/(x − 1) near x = 1. What is its limit as x → 1?

    • 0
    • does not exist
    • 7