Limits with absolute value and trig

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari works with the sine limit near zero. What is the limit of sin(3x)/(2x) as x → 0?

   3/2
2. 2.

   Bo works with the sine limit near zero. What is the limit of sin(5x)/(4x) as x → 0?

   5/4
3. 3.

   Esme works with the sine limit near zero. What is the limit of sin(2x)/(3x) as x → 0?

   2/3
4. 4.

   Jun works with the sine limit near zero. What is the limit of sin(6x)/(5x) as x → 0?

   6/5
5. 5.

   Kira studies f(x) = 3|x − 2|/(x − 2) + 1. What is the limit of f(x) as x → 2⁻?

   -2
6. 6.

   Luz studies f(x) = 4|x + 1|/(x + 1) + 2. What is the limit of f(x) as x → -1⁻?

   -2
7. 7.

   Milo studies f(x) = 2|x − 5|/(x − 5) + 8. What is the limit of f(x) as x → 5⁻?

   6
8. 8.

   Noah studies f(x) = 6|x − 3|/(x − 3) − 1. What is the limit of f(x) as x → 3⁻?

   -7
9. 9.

   Pia works with the tangent limit near zero. What is the limit of tan(4x)/(3x) as x → 0?

   4/3
10. 10.

    Ren works with the tangent limit near zero. What is the limit of tan(7x)/(2x) as x → 0?

    7/2