Find limits of rational functions as x → ∞

Question 1

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

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

Question 2

Find the limit as x → ∞ of (−4x² + 3x + 3)/(9x² − 6x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 3

What happens to (2x² + 1)/(5x² − 3) as x → ∞?

• A. 0
• B. 2/5
• C. No finite limit (it grows without bound)

Question 4

Find the limit as x → ∞ of (9x² + 3)/(8x² − 7x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 5

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

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

Question 6

Find the limit as x → ∞ of (4x² + 8x + 3)/(4x² − 7x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 7

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

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

Question 8

Find the limit as x → ∞ of (7x² − 7x + 3)/(4x² − 7x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 9

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

• A. 0
• B. 3/5
• C. No finite limit (it grows without bound)

Question 10

Find the limit as x → ∞ of (−7x² + 8x + 3)/(5x² − x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 11

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

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

Question 12

Find the limit as x → ∞ of (−7x² − 2x + 3)/(x² − 8x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 13

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

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

Question 14

Find the limit as x → ∞ of (8x² + 3)/(6x² + 4x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 15

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

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

Question 16

Find the limit as x → ∞ of (8x² + 3)/(7x² − 9x − 1). Give a fraction if needed.

Answer (as a fraction)