For what values of x, if any, does #f(x) = x/(xe^x-3) # have vertical asymptotes?

1 Answer
mason m
Jan 2, 2016

#x~~1.04991#

Explanation:

A vertical asymptote in a rational function will occur when the denominator is equal to #0#. Set the denominator equal to #0# and solve for #x#.

#xe^x-3=0#

This cannot be solved analytically. I recommend graphing the function and tracing the zero.

graph{xe^x-3 [-10, 10, -5, 5]}

Since #x~~1.04991#, that is the spot where there is a vertical asymptote.

graph{x/(xe^x-3) [-10, 10, -5, 5]}

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