Limits with absolute value and trig

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari wants the limit of sin(x − 4)/(x² − 16) as x → 4. Direct substitution fails. What is the limit?

   1/8
2. 2.

   Bo wants the limit of sin(x − 5)/(x² − 25) as x → 5. Direct substitution fails. What is the limit?

   1/10
3. 3.

   Esme wants the limit of sin(x − 7)/(x² − 49) as x → 7. Direct substitution fails. What is the limit?

   1/14
4. 4.

   Jun wants the limit of sin(x − 9)/(x² − 81) as x → 9. Direct substitution fails. What is the limit?

   1/18
5. 5.

   Kira wants the limit of sin(4x)/(x² + 5x) as x → 0. What is it?

   4/5
6. 6.

   Milo wants the limit of sin(2x)/(x² + 9x) as x → 0. What is it?

   2/9
7. 7.

   Noah wants the limit of sin(10x)/(x² + 3x) as x → 0. What is it?

   10/3
8. 8.

   Ren looks at 3 + x sin(2/x) as x shrinks toward zero, where the inside 2/x grows without bound. What is its limit?

   • 3
   • does not exist
   • 4
9. 9.

   Tala looks at sin(2/x) as x shrinks toward zero, where the inside 2/x grows without bound. What is its limit?

   • 0
   • does not exist
   • 1
10. 10.

    Zee looks at 4 + cos(2/x) as x shrinks toward zero, where the inside 2/x grows without bound. What is its limit?

    • does not exist
    • 5
    • 4