Limits that need factoring or rationalizing

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   A cart speeds up: s(t) = 4t² meters after t seconds. Bo finds the limit of (s(t) − s(5))/(t − 5) as t → 5. What is it, in m/s?

   40
2. 2.

   A sled slides downhill: s(t) = 2.5t² meters after t seconds. Esme finds the limit of (s(t) − s(4))/(t − 4) as t → 4. What is it, in m/s?

   20
3. 3.

   A scooter rolls downhill: s(t) = 1.5t² meters after t seconds. Jun finds the limit of (s(t) − s(6))/(t − 6) as t → 6. What is it, in m/s?

   18
4. 4.

   Kira wants the limit of (x² + kx − 6)/(x − 2) as x → 2 to be a number. The top must be 0 at x = 2. What is k?

   1
5. 5.

   Luz wants the limit of (x² + kx − 21)/(x − 3) as x → 3 to be a number. The top must be 0 at x = 3. What is k?

   4
6. 6.

   Milo wants the limit of (x² + kx − 5)/(x − 1) as x → 1 to be a number. The top must be 0 at x = 1. What is k?

   4
7. 7.

   Noah wants the limit of (x² + kx − 10)/(x − 5) as x → 5 to be a number. The top must be 0 at x = 5. What is k?

   -3
8. 8.

   Pia looks at the limit of (x² − 16)/(x − 4) as x → 4 before working it out. Which first step fits?

   • substitute directly
   • combine the fractions
   • multiply by the conjugate
   • factor and cancel
9. 9.

   Ren looks at the limit of (√x − 3)/(x − 9) as x → 9 before working it out. Which first step fits?

   • factor and cancel
   • multiply by the conjugate
   • substitute directly
   • combine the fractions
10. 10.

    Tala looks at the limit of (1/x − 1/2)/(x − 2) as x → 2 before working it out. Which first step fits?

    • multiply by the conjugate
    • substitute directly
    • factor and cancel
    • combine the fractions