How do you find the asymptotes for #y = (5e^x)/ ((e^x)  8)#?
1 Answer
Feb 24, 2017
Vertical asymptote at
Horizontal asymptotes at:
Explanation:
The vertical asymptote is found when
Solve for
Vertical asymptote at
Finding horizontal asymptotes :

#N(x) = 5e^x = 0; e^x = 0; ln e^x = ln 0; x = ln 0# which is undefined. By definition logarithms are positive:#x > 0# This means there is a horizontal asymptote at#y = 0# 
#lim x>oo (5e^x/e^x)/(e^x/e^x  8/e^x) = 5/(10) = 5# so there is a horizontal asymptote at#y = 5#
Summary:
Vertical asymptote at
Horizontal asymptotes at: