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

1 Answer
Bill Jorgensen
Jun 9, 2018

asymptote at:

#x=ln2 ~~0.693#

No removable discontinuities.

Explanation:

#f(x)= (2x-e^x)/(2-e^x)#

There are no factors that cancel in the numerator and denominator so there are no removable discontinuities (holes). To find the asymptote(s) find when the function is undefined, i.e. #(2x-e^x)/0#

#2-e^x=0#

#e^x=2#

#ln(e^x)=ln2#

#x=ln2 ~~0.693#

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