How do you show the limit does not exist limx→4x−4x2−8x+16lim_(x->4)(x-4)/(x^2-8x+16) ?

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Mathematics

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How do you show the limit does not exist limx→4x−4x2−8x+16lim_(x->4)(x-4)/(x^2-8x+16) ?

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Анонимid Анонимid · Answer 1

Анонимid Анонимid

[tex]\lim\limits_{x\to4}\frac{x-4}{x^2-8x+16}=\lim\limits_{x\to4}\frac{x-4}{(x-4)^2}=\lim\limits_{x\to4}\frac{1}{x-4}\\\\\lim\limits_{x\to4^-}\frac{1}{x-4}=\frac{1}{0^-}=-\infty\\\\\lim\limits_{x\to4^+}\frac{1}{x-4}=\frac{1}{0^+}=\infty[/tex]

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