To solve the problem, let's first analyze the given sets $A$ and $B$:

• $A = \{x \mid -5 < x^3 < 5\}$
• $B = \{-3, -1, 0, 2, 3\}$

We need to determine the intersection $A \cap B$.

Step-by-Step Solution:

1. Determine Set A:

   • $-5 < x^3 < 5$
   • Solve for $x$:
     • For $x^3 = -5$, $x \approx -1.710$
     • For $x^3 = 5$, $x \approx 1.710$
   • So, $A \approx (-1.710, 1.710)$

2. Determine Intersection with Set B:

   • We check which elements of $B$ fall within the interval $(-1.710, 1.710)$:
     • $-3 \notin (-1.710, 1.710)$
     • $-1 \in (-1.710, 1.710)$
     • $0 \in (-1.710, 1.710)$
     • $2 \notin (-1.710, 1.710)$
     • $3 \notin (-1.710, 1.710)$

So, the intersection $A \cap B$ is $\{-1, 0\}$.

Conclusion:

The correct answer is:

• Option A: $\{-1, 0\}$

Would you like further details or have any questions?

Here are 5 numbered questions you might ask next:

1. How do you solve inequalities involving cubic functions?
2. What are the steps to determine set intersections?
3. Can you explain the interval notation for set descriptions?
4. How do you find the cube root of a number?
5. What are some properties of intersections in set theory?

Tip: When solving set problems, always clearly define each set and carefully determine the elements that satisfy all given conditions.