Question

Evaluate the limit

n³/(2n²-1) - n²/(2n-1)
A) The limit is 0.
B) The limit is 1.
C) The limit is [infinity] (infinity).
D) The limit is undefined.

Answer 1

The limit of the function n³/(2n²-1) - n²/(2n-1) as n approaches infinity is 0,(A) because the highest power of n dominates and the resulting limits of each term cancel out.

Step-by-step explanation:

The student has asked to evaluate the limit of the expression as n approaches infinity for the function n³/(2n²-1) - n²/(2n-1). To find this limit, we divide by the highest power of n in the denominator in each term. Doing this simplifies the expression in each term to 1/2 - 1/2 in the limit as n approaches infinity. This is because the terms with lower powers of n become negligible compared to the highest power of n. Therefore, the limit of both terms is 1/2, but since the expression is n³/(2n²-1) minus n²/(2n-1), the actual limit is 0.