Respuesta :
[tex]\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
\lim\limits_{x\to 2}\ \cfrac{x^2-4}{x-2}
\\\\\\
\cfrac{x^2-4}{x-2}\implies \cfrac{x^2-2^2}{x-2}\implies \cfrac{(x-2)(x+2)}{x-2}\implies x+2
\\\\\\
\lim\limits_{x\to 2}\ x+2\implies 4[/tex]
The limit of the function [tex](x^{2} -4)/(x-2)[/tex] when x approaches to 2 is 4.
What is limit?
The limit of a function is a fundamental concept in calculas. It is basically the value of that function approaches as its input approaches to given value. It helps in finding whether a function is continuous or not.
How to find limit of function?
The given function whose limit is to be find is [tex](x^{2} -4)/(x-2)[/tex].
We have to find the limit of that funtion as x approaches to 2.
f(x)=[tex](x^{2} -4)/(x-2)[/tex]
Limit of f(x)=[tex]\lim_{x \to \2} (x^{2} -4)/(x-2)[/tex]
[tex]x^{2} -4[/tex]=[tex](x^{2} -2^{2} )[/tex]
=(x+2)(x-2)
Put this value in limi.
[tex]\lim_{x \to \2}(x+2)(x-2)/(x-2)[/tex]
=[tex]\lim_{x \to \0} (x+2)[/tex]
Put x=2 in limit
=2+2
=4
Hence the limit of function [tex](x^{2} -4)/(x-2)[/tex] is 4.
Learn more about limit at https://brainly.com/question/23343679
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