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

Answer 1

#x~~1.04991#

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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Answer 2

The function f(x) = x/(xe^x-3) has vertical asymptotes at x = 0 and x = 3.

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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.

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.

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.

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.

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