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For what values of x, if any, does #f(x) = e^x/(e^x-e^(2x)) # have vertical asymptotes?

Answer 1

Christopher Agresta

#x=0#

In a rational function such as this, vertical asymptotes occur when the denominator is equal to #0#.

Set the denominator equal to #0#.

#e^x-e^(2x)=0#

#e^x=e^(2x)#

#x=2x#

#x=0#

The vertical asymptote occurs when #x=0#. Check a graph:

graph{(e^x)/(e^x-e^(2x)) [-14.24, 14.24, -7.12, 7.12]}

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Answer 2

Luke Alvarez

The function f(x) = e^x/(e^x-e^(2x)) has vertical asymptotes at x = 0 and x = -∞.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.