SOLUTION: Find the horizontal and vertical asymptotes of the following: A) f(x)= 2x+3/x+2 B) g(x)= 5x / x^2+1

Question 92310: Find the horizontal and vertical asymptotes of the following:
A) f(x)= 2x+3/x+2
B) g(x)= 5x / x^2+1
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
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 ~> +] (2x + 3)/(x + 2)
lim[x ~> +] 2(x^0)/(x^0) H' Theory
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 ~> +] 5x / (x^2 + 1)
lim[x ~> +] 5/(2x) H' Theory
(5/2) * lim[x ~> +] 1/x
(5/2)(0) = 0
But: g(0) = 0 ... no asymptote

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