The function $g$ is defined for all real numbers.

What is a reasonable estimate for $\lim _{x \rightarrow 2} g(x)$ ?
Choose 1 answer:
(A) -2.4
(B) -2
(C) 1.5
(D) 2
(E) The limit doesn't exist.

Question

The function $g$ is defined for all real numbers.

What is a reasonable estimate for $\lim _{x \rightarrow 2} g(x)$ ?
Choose 1 answer:
(A) -2.4
(B) -2
(C) 1.5
(D) 2
(E) The limit doesn't exist.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the limit of $g(x)$ as $x$ approaches 2, we need to observe the behavior of the function $g(x)$ near $x = 2$. ‖ ‖ step 2 ⋮ From the graph, we see that as $x$ approaches 2 from both the left and the right, the function $g(x)$ approaches the value at the open circle, which is $1.5$. ‖ ‖ step 3 ⋮ Therefore, the limit of $g(x)$ as $x$ approaches 2 is $1.5$. ‖ ***C*** ∻Key Concept∻ ⚹Limit of a function⚹ ∻Explanation∻ ⚹The limit of a function as $x$ approaches a certain value is the value that the function approaches as $x$ gets closer to that value. In this case, the graph shows that $g(x)$ approaches $1.5$ as $x$ approaches 2.⚹◊What is the definition of a limit of a function as x approaches a specific value?⍭ Generate me a similar question◊

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