Question 92310
A) f(x)= (2x + 3)/(x + 2)
Vertical Asymptote:
x = -2 because of the denominator
Horizontal Asymptope:
y = 2 derived from graphing or:
lim[x ~> +{{{inf}}}] (2x + 3)/(x + 2)
lim[x ~> +{{{inf}}}] 2(x^0)/(x^0) H' Theory
2
{{{graph(300,300,-5,5,-5,5,(2x + 3)/(x + 2))}}}
B) g(x)= 5x / (x^2 + 1)
Vertical Asymptote:
none because of the denominator
Horizontal Asymptope:
y = 0 derived from graphing or:
lim[x ~> +{{{inf}}}] 5x / (x^2 + 1)
lim[x ~> +{{{inf}}}] 5/(2x) H' Theory
(5/2) * lim[x ~> +{{{inf}}}] 1/x
(5/2)(0) = 0
But: g(0) = 0 ... no asymptote
{{{graph(800,200,-20,20,-2.5,2.5,5x / (x^2 + 1))}}}