contestada

Consider the function Upper F (x )equals StartFraction f (x )Over g (x )EndFractionF(x)= f(x) g(x) with ​g(a)equals=0. Does F necessarily have a vertical asymptote at xequals=​a? Explain your reasoning.

Respuesta :

pedrocarratore

Answer:

No, not necessarily

Step-by-step explanation:

If g(a) = 0, it is not necessarily that F(x) will have a vertical asymptote at x = ​a

For instance, assume the following conditions:

[tex]F(x) = \frac{f(x)}{g(x)}\\f(x) = x^3*(x-a)\\g(x) = x-a[/tex]

In this conditions, g(a) = 0. F(a), however, can be written as:

[tex]F(x) = \frac{x^3*(x-a)}{x-a}\\F(a) = a^3[/tex]

In this particular case, F(x = a) does not show a vertical asymptote.