Using perfect squares simplification, it is found that the value of the desired limit is of -4.
It is the value of a function as x approach
In this problem, the limit we want to find is given by:
[tex]\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2}[/tex]
If we just replace x by -2, we end with an undetermined limit, as we have 0/0.
However, the perfect square simplification states that:
a² - b² = (a - b)(a + b).
Hence:
x² - 4 = (x + 2)(x - 2).
Then:
[tex]\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x + 2)(x - 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 - 2 = -4[/tex]
Hence, the value of the desired limit is of -4.
More can be learned about limits at https://brainly.com/question/26270080
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