The function f(x) = 2 / (lnx -6) has a horixontal asymptote at y = ? and a vertical asymptote at x = ?

Answer 1

f(x) = 2 / [(lnx) - 6]

Lim x→∞ of {2 / [(lnx) - 6]} = 0/∞ = 0
The horizontal asymptote is y = 0.

A vertical asymptote occurs when the denominator is zero. That will occur when:

lnx - 6 = 0
lnx = 6
x = e^6

The vertical asymptote is x = e^6.