Question

What is Limit of StartFraction x squared minus 4 Over x + 2 EndFraction as x approaches negative 2?

Answer 1

Using perfect squares simplification, it is found that the value of the desired limit is of -4.

When is a limit?

It is the value of a function as x approach

In this problem, the limit we want to find is given by:

$\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2}$

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:

$\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x + 2)(x - 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 - 2 = -4$

Hence, the value of the desired limit is of -4.

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

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