1. 已知集合 $A=\left\{x \mid-5

Q: 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. $\{-1,0,2\}$

∻Solution by Steps∻ ‖ step 1 ⋮ Solve the inequality $-5 < x^3 < 5$. ‖ ‖ 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 $A$.⚹◊What is the intersection of the sets $A$ and $B$ defined as $A=\left\{x \mid -5

Question

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. $\{-1,0,2\}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Solve the inequality $-5 < x^3 < 5$. ‖ ‖ 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 $A$.⚹◊What is the intersection of the sets $A$ and $B$ defined as $A=\left\{x \mid -5

Sia