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Sagot :

From the given table, we have that the lateral limits of f(x) as x -> 3 are different, hence the limit of f(x) does not exist at x = 3.

What is a limit?

A limit is given by the value of function f(x) as x tends to a value. For the limit to exist, the lateral limits have to be the same, as follows:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x)[/tex]

In this problem, we have that:

  • To the left of x = 3, that is, for values that are less than x = 3, f(x) - > -3.
  • To the right of x = 3, that is, for values that are greater than x = 3, f(x) -> 4.

Hence the lateral limits are given as follows:

  • [tex]\lim_{x \rightarrow 3^-} f(x) = -3[/tex]
  • [tex]\lim_{x \rightarrow 3^+} f(x) = 4[/tex]

Since the lateral limits are different, the limit does not exist.

More can be learned about lateral limits at https://brainly.com/question/26270080

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