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
Obviously, the graphs of
Graphing:
graph{(e^x)/(1-e^(3x^2-x)) [-18.02, 18.03, -9.01, 9.01]}