Find limits of rational functions as x → ∞

Question 1

What happens to (2x + 1)/(3x² − 3) as x → ∞?

• A. 0
• B. 2/3
• C. No finite limit (it grows without bound)

Question 2

Find the limit as x → ∞ of (9x² + 3)/(4x² − 2x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 3

What happens to (6x³ + 2)/(x² − 3) as x → ∞?

• A. 0
• B. 6
• C. No finite limit (it grows without bound)

Question 4

Find the limit as x → ∞ of (−5x² − 7x + 3)/(9x² − 3x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 5

What happens to (3x² + 1)/(6x² − 3) as x → ∞?

• A. 0
• B. 1/2
• C. No finite limit (it grows without bound)

Question 6

Find the limit as x → ∞ of (x² − 7x + 3)/(6x² + 9x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 7

What happens to (6x² + 1)/(5x² − 3) as x → ∞?

• A. 0
• B. 6/5
• C. No finite limit (it grows without bound)

Question 8

Find the limit as x → ∞ of (−x² − 4x + 3)/(9x² − x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 9

What happens to (4x² + 1)/(5x² − 3) as x → ∞?

• A. 0
• B. 4/5
• C. No finite limit (it grows without bound)

Question 10

Find the limit as x → ∞ of (−x² − 7x + 3)/(3x² − 3x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 11

What happens to (6x³ + 2)/(6x² − 3) as x → ∞?

• A. 0
• B. 1
• C. No finite limit (it grows without bound)

Question 12

Find the limit as x → ∞ of (7x² − 5x + 3)/(x² − 5x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 13

What happens to (4x + 1)/(2x² − 3) as x → ∞?

• A. 0
• B. 2
• C. No finite limit (it grows without bound)

Question 14

Find the limit as x → ∞ of (3x² + x + 3)/(8x² − 4x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 15

What happens to (x³ + 2)/(5x² − 3) as x → ∞?

• A. 0
• B. 1/5
• C. No finite limit (it grows without bound)

Question 16

Find the limit as x → ∞ of (4x² + 4x + 3)/(3x² − 5x − 1). Give a fraction if needed.

Answer (as a fraction)