Question

Use the comparison theorem to determine x/x³ ≤1.

A) Monotonic sequence
B) Limit comparison test
C) Ratio test
D) Absolute convergence

Answer 1

The comparison theorem is used to determine when x/x³ ≤ 1. The correct solution to the inequality is x > 1 and x < -1.

Step-by-step explanation:

The question is asking to determine when x/x³ ≤ 1 using the comparison theorem. To solve this inequality, we can simplify it by dividing both sides by x³. This gives us 1/x² ≤ 1. Rearranging the inequality, we have 1 ≤ x². Taking the square root of both sides, we get 1 ≤ |x|. So, the inequality holds true for x > 1 and x < -1. Therefore, the correct answer is A) Monotonic sequence.