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
(द) 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
(द) 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 analyze the behavior of the function near $x = 2$. ‖ ‖ step 2 ⋮ From the graph, as $x$ approaches 2 from both the left and the right, the function $g(x)$ approaches the value at the hole, which is at the point (2, 1). ‖ ‖ step 3 ⋮ Therefore, $\lim_{x \rightarrow 2} g(x) = 1$. ‖ ‖ step 4 ⋮ The separate point plotted at (2, -3) does not affect the limit because the limit depends on the values of $g(x)$ as $x$ approaches 2, not the value of $g(2)$. ‖ ***C*** ∻Key Concept∻ ⚹Limit of a function⚹ ∻Explanation∻ ⚹The limit of a function as $x$ approaches a certain value is determined by the values of the function near that point, not necessarily the value of the function at that point.⚹◊What is the definition of a limit in calculus?⍭ Generate me a similar question◊

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