# How do you find the asymptotes for y=x*ln[e + (1/x)] ?

Jun 27, 2018

Asymptote at $x = - \frac{1}{e} , 0$
There is an asymptote at $x = 0$ because at this point the function is undefined as $\frac{1}{0}$ is undefined. There is also an asymptote at
$e + \frac{1}{x} = 0$ as the $\ln$ function is undefined at $0$
$e + \frac{1}{x} = 0 , e x + 1 = 0 , e x = - 1 x = - \frac{1}{e}$