Question

Math

Posted 4 months ago

```
Functions $g$ and $h$ are graphed.
Find $\lim _{x \rightarrow-2}(g(x) h(x))$.
Choose 1 answer:
(A) 0
(B) 2
(C) 4
(D) 8
(E) The limit doesn't exist.
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

To find the limit of the product of two functions $g(x)$ and $h(x)$ as $x$ approaches $-2$, we need to evaluate $g(-2)$ and $h(-2)$

step 2

From the graph of $g(x)$, as $x$ approaches $-2$, the value of $g(x)$ is $2$ (since there is a closed circle at $(-2, 2)$)

step 3

From the graph of $h(x)$, as $x$ approaches $-2$, the value of $h(x)$ is $2$ (since the line is continuous and passes through $(-2, 2)$)

step 4

Therefore, the limit of the product $g(x)h(x)$ as $x$ approaches $-2$ is $g(-2) \cdot h(-2) = 2 \cdot 2 = 4$

Answer

4

Key Concept

Limit of a product of functions

Explanation

To find the limit of the product of two functions as $x$ approaches a certain value, evaluate each function at that value and multiply the results.

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