Respuesta :

[tex]\lim \limits_{x \to2} \frac{ {x}^{2} - 4 }{x - 2} \\ = \lim \limits_{x \to2} \frac{ {(x)}^{2} - {(2)}^{2} }{x - 2} \\ = \lim \limits_{x \to2} \frac{ ( x- 2)(x + 2) }{x - 2} \\ = \lim \limits_{x \to2} ( x+ 2) \\ = 2 + 2 \\ = 4[/tex]

Answer:

4

Hope you could understand.

If you have any query, feel free to ask.

cinderofsoulsss

Answer:

The limit of the function as x approaches 2 is 4.

Step-by-step explanation:

This function just simplifies to [tex]x+2[/tex]:

[tex]\frac{x^2-4}{x-2}\\\\\frac{(x+2)(x-2)}{x-2}\\\\x+2[/tex]

That leaves us with this:

​[tex]\lim_{x\to2}x+2[/tex]

This is a simple linear function that can be evaluated at [tex]x=2[/tex]:

[tex]f(x)=x+2\\f(2)=2+2\\f(2)=4[/tex]

The values also exist on either side of this point.

[tex]f(1.999)=3.999\\f(2.001)=4.001[/tex]

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