How do you find the asymptotes for #y = (4 e^x)/(e^x - 2)#?

1 Answer
Jan 29, 2016

Answer:

Vertical asymptote at #x=ln2#.
Horizontal asymptote at #y=4#.

Explanation:

There exists vertical asymptotes at points that set the denominator to zero,
that is, when #e^x-2=0# or when #e^x=2# #=>x=ln2#.

Horizontal asymptotes occur at #y=lim_(x->+-oo)[(4e^x)/(e^x-2)]=4#

The graph of the function verifies this.

graph{(4e^x)/(e^x-2) [-10.59, 11.91, -4.14, 7.11]}