Consider the graph of function $h$.

Which limit expressions agree with the graph?
Choose all answers that apply:
A) $\lim _{x \rightarrow-4} h(x)=-2$

В $\lim _{x \rightarrow 0^{+}} h(x)=2$
(c) $\lim _{x \rightarrow 4^{-}} h(x)=2$

D None of the above

Question

Consider the graph of function $h$.

Which limit expressions agree with the graph?
Choose all answers that apply:
A) $\lim _{x \rightarrow-4} h(x)=-2$

В $\lim _{x \rightarrow 0^{+}} h(x)=2$
(c) $\lim _{x \rightarrow 4^{-}} h(x)=2$

D None of the above

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the limit as $x$ approaches $-4$, we observe the graph. The function $h(x)$ is not defined at $x = -4$ since there is no point or segment at $x = -4$. Therefore, $ \lim_{x \rightarrow -4} h(x)$ does not exist. ‖ ‖ step 2 ⋮ To determine the limit as $x$ approaches $0$ from the right, we observe the graph. The function $h(x)$ has a closed circle at $(0, 2)$, indicating that $h(0) = 2$. Therefore, $ \lim_{x \rightarrow 0^{+}} h(x) = 2$. ‖ ‖ step 3 ⋮ To determine the limit as $x$ approaches $4$ from the left, we observe the graph. The function $h(x)$ has an open circle at $(4, 2)$, indicating that $h(4)$ is not defined at this point. However, as $x$ approaches $4$ from the left, the function value approaches $2$. Therefore, $ \lim_{x \rightarrow 4^{-}} h(x) = 2$. ‖ ∻[question number] Answer∻ ***B, C*** ∻Key Concept∻ ⚹Limit of a function⚹ ∻Explanation∻ ⚹The limit of a function as $x$ approaches a point is the value that the function approaches as $x$ gets closer to that point. If the function is defined and continuous at that point, the limit is simply the function's value at that point.⚹◊What is the definition of a limit in calculus⍭ Generate me a similar question◊

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