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.

Question

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.

Accepted Answer

∻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.⚹◊What is the product rule for finding the limit of the product of two functions as x approaches a certain value?⍭ Generate me a similar question◊

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