# What are the asymptotes and removable discontinuities, if any, of #f(x)=e^x/(1-e^(3x^2-x))#?

##### 1 Answer

Mar 1, 2018

No discontinuities.

Vertical asymptotes at

Horizontal asymptote at

#### Explanation:

To find the vertical asymptotes, we equate the denominator to

Here,

So we find vertical asymptote is at

To find the horizontal asymptote, we must know one crucial fact: **all exponential functions have horizontal asymptotes at #y=0#**

Obviously, the graphs of

Graphing:

graph{(e^x)/(1-e^(3x^2-x)) [-18.02, 18.03, -9.01, 9.01]}