Question

Math

Posted about 2 months ago

```
1. 已知集合 $A=\left\{x \mid-5<x^{3}<5\right\}, B=\{-3,-1,0,2,3\}$, 则 $A \cap B=$ （）
A. $\{-1,0\}$
B. $\{2,3\}$
C. $\{-3,-1,0\}$
D. $\{-1,0,2\}$
```

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Answer from Sia

Posted about 2 months ago

Solution by Steps

step 2

Taking the cube root of each part, we get $-5^{1/3} < x < 5^{1/3}$

step 3

The cube root of 5 is approximately 1.71, so the interval is $-1.71 < x < 1.71$

step 4

Now, we find the intersection of the set $A = \{x \mid -5 < x^3 < 5\}$ with the set $B = \{-3, -1, 0, 2, 3\}$

step 5

The elements of $B$ that lie within the interval $-1.71 < x < 1.71$ are $-1$ and $0$

step 6

Therefore, $A \cap B = \{-1, 0\}$

A

Key Concept

Intersection of Sets

Explanation

The intersection of two sets is the set containing all elements that are common to both sets. In this problem, we found the elements of set $B$ that lie within the interval defined by set $A$.

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