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 ball rolls down a ramp: s(t) = 3t² meters after t seconds. Ari finds the limit of (s(t) − s(3))/(t − 3) as t → 3. What is it, in m/s?

   18
2. 2.

   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
3. 3.

   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
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.

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

   • factor and cancel
   • multiply by the conjugate
   • combine the fractions
   • substitute directly
8. 8.

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

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

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

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

    Zee looks at the limit of (x² + 1)/(x + 1) as x → 2 before working it out. Which first step fits?

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