Limits at infinity and end behavior

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari wants the limit of (3x² + 1)/(2x² − 5) as x → ∞. What is it?

   3/2
2. 2.

   Bo wants the limit of (5x² − 4)/(7x² + 3) as x → ∞. What is it?

   5/7
3. 3.

   Esme wants the limit of (-6x² + 2)/(4x² + 9) as x → ∞. What is it?

   -3/2
4. 4.

   Jun wants the limit of (8x² + 6)/(3x² − 1) as x → ∞. What is it?

   8/3
5. 5.

   Kira studies f(x) = 4 + 6/x for huge x. What is the limit of f(x) as x → ∞?

   4
6. 6.

   Luz studies f(x) = -2 + 5/x² for huge x. What is the limit of f(x) as x → ∞?

   -2
7. 7.

   Noah studies f(x) = 1 + 9/x³ for huge x. What is the limit of f(x) as x → ∞?

   1
8. 8.

   x = 10 gives 2.555556; x = 100 gives 2.050505; x = 1000 gives 2.005005; x = 10000 gives 2.0005. Pia fills in the table shown for bigger and bigger x. What limit does f(x) head to as x → ∞?

   2
9. 9.

   x = 10 gives 4.807692; x = 100 gives 4.998001; x = 1000 gives 4.99998; x = 10000 gives 5. Ren fills in the table shown for bigger and bigger x. What limit does f(x) head to as x → ∞?

   5
10. 10.

    x = 10 gives -0.333333; x = 100 gives -0.482587; x = 1000 gives -0.498251; x = 10000 gives -0.499825. Tala fills in the table shown for bigger and bigger x. What limit does f(x) head to as x → ∞?

    -0.5