Find all vertical asymptotes, x=a, of the following functions. For each value of a, evaluate lim x-a^+,lim x-a^-,and limx-a

Question

Find all vertical asymptotes, x=a, of the following functions. For each value of a, evaluate lim x->a^+,lim x->a^-,and limx->a

anonymous · Answer

$$f(x) = \frac{ x^3-10x^2+16x }{ x^2-8x }$$

anonymous · Answer

(a) Find all vertical asymptotes  x=a
(b)Evaluate limits at $$\lim_{x \rightarrow a^+}$$
$$\lim_{x \rightarrow a^-}$$
$$\lim_{x \rightarrow a}$$

anonymous · Answer

I know that to find a vertical asymptote, $$h(x)=\frac{ f(x) }{ g(x) }$$
where if the demnominatopr at g(x) is 0 and the numerator at f(c) is not zero than h is a vertical asymptote where x=c.

anonymous · Answer

Factoring out f(x):
$$f(x) = \frac{x^3-10x^2+16x} {x^2-8x}$$
$$=\frac{x(x-2)(x-8)}{x(x-8)}$$
When x = 8 g(x) is zero and f(x) is not zero
so I would have a vertical asymptote at x=8

anonymous · Answer

Is this right so far?