The limit of h(x) as x tends to 2 is equal to 0.
How to get the limit of h(x) when x tend to 2?
Remember that a limit is not the same as an evaluation, the limit studies the behavior of the function near the value, not in x = 2.
While we can see that h(2) = 3 (we have a jump there). We can see that around x = 2 the function tends to zero.
From that, we conclude that:
[tex]\lim_{x \to \ 2} h(x) = 0.[/tex]
Then the correct option is the first one.
If you want to learn more about limits:
https://brainly.com/question/5313449
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