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

What is a reasonable estimate for $\lim _{x \rightarrow 0} h(x) ?$

Choose 1 answer:
(A) -5
(B) 4
(C) 5
(D) The limit doesn't exist

Q: The function $h$ is defined for all real numbers. What is a reasonable estimate for $\lim _{x \rightarrow 0} h(x) ?$ Choose 1 answer: (A) -5 (B) 4 (C) 5 (D) The limit doesn't exist

∻Solution by Steps∻ ‖ step 1 ⋮ To find the limit $\lim_{x \to 0} h(x)$, we need to analyze the behavior of the function $h(x)$ as $x$ approaches 0. ‖ ‖ step 2 ⋮ From the graph, we observe that there is an open circle at $(0, -5)$ and a closed circle at $(0, 5)$. ‖ ‖ step 3 ⋮ The open circle at $(0, -5)$ indicates that $h(0) = -5$ is not included in the function's value. ‖ ‖ step 4 ⋮ The closed circle at $(0, 5)$ indicates that $h(0) = 5$ is the value of the function at $x = 0$. ‖ ‖ step 5 ⋮ Therefore, the limit $\lim_{x \to 0} h(x)$ is determined by the value at the closed circle, which is $5$. ‖ ***C*** ∻Key Concept∻ ⚹Limit of a function⚹ ∻Explanation∻ ⚹The limit of a function as $x$ approaches a certain value is determined by the value the function approaches, which is indicated by the closed circle on the graph.⚹◊What is the relationship between the maximum and minimum points of a function and the limit as x approaches a particular value?⍭ Generate me a similar question◊

Question

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

What is a reasonable estimate for $\lim _{x \rightarrow 0} h(x) ?$

Choose 1 answer:
(A) -5
(B) 4
(C) 5
(D) The limit doesn't exist

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the limit $\lim_{x o 0} h(x)$, we need to analyze the behavior of the function $h(x)$ as $x$ approaches 0. ‖ ‖ step 2 ⋮ From the graph, we observe that there is an open circle at $(0, -5)$ and a closed circle at $(0, 5)$. ‖ ‖ step 3 ⋮ The open circle at $(0, -5)$ indicates that $h(0) = -5$ is not included in the function's value. ‖ ‖ step 4 ⋮ The closed circle at $(0, 5)$ indicates that $h(0) = 5$ is the value of the function at $x = 0$. ‖ ‖ step 5 ⋮ Therefore, the limit $\lim_{x o 0} h(x)$ is determined by the value at the closed circle, which is $5$. ‖ ***C*** ∻Key Concept∻ ⚹Limit of a function⚹ ∻Explanation∻ ⚹The limit of a function as $x$ approaches a certain value is determined by the value the function approaches, which is indicated by the closed circle on the graph.⚹◊What is the relationship between the maximum and minimum points of a function and the limit as x approaches a particular value?⍭ Generate me a similar question◊

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