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

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 of $h(x)$ as $x$ approaches 0, we need to analyze the behavior of the function $h(x)$ near $x = 0$. ‖ ‖ step 2 ⋮ From the graph, we observe that as $x$ approaches 0 from the left, $h(x)$ approaches 5. Similarly, as $x$ approaches 0 from the right, $h(x)$ also approaches 5. ‖ ‖ step 3 ⋮ Since the function $h(x)$ approaches the same value (5) from both sides of $x = 0$, we can conclude that the limit exists and is equal to 5. ‖ ‖ step 4 ⋮ Therefore, $ \lim_{x \rightarrow 0} h(x) = 5 $. ‖ ∻Answer∻ ⚹ (C) 5 ⚹ ∻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 function $h(x)$ approaches 5 as $x$ approaches 0 from both sides, so the limit is 5.⚹◊What is the formula for calculating the limit as $x$ approaches $a$ for a function $h(x)$?⍭ Generate me a similar question◊

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