Question

What is the limit of f(x) / (x³ - 1) as x approaches 1?

a) [infinity]
b) 0
c) 1
d) Indeterminate

Answer 1

Option d is correct option. The limit of the function as x approaches 1 results in an indeterminate 0/0 form. Without additional information on f(x), the specific value of the limit cannot be determined, making the correct answer indeterminate.

Step-by-step explanation:

The question asks about the limit of a function as x approaches 1. Specifically, we're looking at the limit of f(x) / (x³ - 1) as x -> 1. To solve this, we might try to substitute x=1 directly into the denominator, but this gives us 0 since 1³ - 1 = 0. The expression becomes a form of 0/0, which is an indeterminate form.

This means we cannot determine the limit by direct substitution. Instead, we should apply tools such as factoring, L'Hôpital's rule, or other algebraic manipulation to simplify the expression and find the limit. Without additional information about f(x), we cannot determine a specific value for the limit; thus, the correct answer would be indeterminate, which is option d.