Question

Math

Posted 5 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 5 months ago

Solution by Steps

step 1

To find $\lim_{x \rightarrow -2} (g(x) h(x))$, we first need to determine the values of $g(x)$ and $h(x)$ as $x$ approaches -2

step 2

From the graph of $g(x)$, as $x$ approaches -2, $g(x)$ approaches 4

step 3

From the graph of $h(x)$, as $x$ approaches -2, $h(x)$ is a constant value of 2

step 4

Now, we multiply the limits of $g(x)$ and $h(x)$ as $x$ approaches -2: $\lim_{x \rightarrow -2} (g(x) h(x)) = \lim_{x \rightarrow -2} g(x) \cdot \lim_{x \rightarrow -2} h(x) = 4 \cdot 2 = 8$

Answer

8

Key Concept

Limit of a product of functions

Explanation

The limit of the product of two functions as $x$ approaches a certain value is the product of the limits of the individual functions as $x$ approaches that value.

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