How to find the vertical assimptote

[transgalactic]

<br /> f(x)=\frac{1}{1+ln|x|}\\<br />
<br /> x\neq \frac{1}{e}\\<br />
<br /> x\neq \frac{-1}{e}\\<br />
<br /> lim_{x-&gt;\frac{1}{e}^+}\frac{1}{1+ln|x|}=\\<br />
<br /> lim_{x-&gt;\frac{1}{e}^-}\frac{1}{1+ln|x|}=\\<br />
i can't immagine ithe values in this function
??

 

[HallsofIvy]

First, 1/e is a postive number so you can just drop the absolute value.

Second, ln e^-1= -1. Since ln(x) is an increasing function, if x< e^-1, ln(x)< -1 and if x> e^-1, ln(x)> -1. That's all you need.