How do you find the asymptotes for $R(x)= (x+2)/(x^2-64)$ ?

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Answer 1 · 2016-12-28T15:19:58

See explanation

The expression becomes undefined at the point where you have:

$("some value")/0$ .

So we have:

$color(blue)(lim_(x^2-64->0^+) =lim_(x->8^+) (x+2)/(x^2-64) ->+oo)$

$color(blue)(lim_(x^2-64->0^-) =lim_(x->8^-) (x+2)/(x^2-64) -> -oo)$

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Now we investigate as $x->+-oo$

As $x$ becomes increasingly positive or negative the less and less influence is applied by the 2 in the numerator and the -64 in the denominator.

Thus the expression tend towards $x/x^2 = 1/(+-x)$

And as $|x| ->oo$ then $1/(|x|) ->0$

$color(blue)(lim_(x->oo^-) (x+2)/(x^2-64)->0^-)$

$color(blue)(lim_(x->oo^+) (x+2)/(x^2-64)->0^+)$
Tony B

How do you find the asymptotes for R(x)= (x+2)/(x^2-64)R(x)= (x+2)/(x^2-64)?