What is the limit, as x -> ∞, of (2x^2)/(x^3)?

What is the limit, as x -> ∞, of (2x^2)/(x^3)?

• A. ∞
• B. 0
• C. 1
• D. -1

Answer: (B)

When a fraction has a higher power in the denominator than in the numerator, it tends to shrink to zero as x grows. Here you can simplify directly: 2x^2/x^3 = 2/x. As x approaches infinity, 2/x becomes arbitrarily small, since you’re dividing a constant by an ever-larger number. Therefore the limit is 0. The positive sign for large x confirms the approach from the positive side, but the value the expression approaches is 0.

When a fraction has a higher power in the denominator than in the numerator, it tends to shrink to zero as x grows. Here you can simplify directly: 2x^2/x^3 = 2/x. As x approaches infinity, 2/x becomes arbitrarily small, since you’re dividing a constant by an ever-larger number. Therefore the limit is 0. The positive sign for large x confirms the approach from the positive side, but the value the expression approaches is 0.