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How do you find the asymptotes for #e^x / x#?

Answer 1

Serenity Jones

At #x=0# and #y=0#

Vertical asymptotes:

Vertical asymptotes are found when the function is not defined. Here, the denominator must be #0# for this to occur.

So when #x=0#, there is an asymptote.

Horizontal asymptotes:

Horizontal asymptotes correspond to the range of a function. #y# is defined for all values of #x#. However, for any value of #x#, #y# can never be #0#.

This is because for so, #e^x=0# for a certain value of #x#. However, as this is not possible, there exists an asymptote at #y=0#.

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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.