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How do you find the limit of #e^(1/x)# as x approaches #0^-#?

Answer 1

Cameron Alexander

#lim_{x to 0^-} e^(1/x)#

#= e ^ (lim_{x to 0^-} 1/x)# because #f(u) = e^u # is a continuous function including through the limit

and #lim_{x to 0^-} 1/x = - oo#

so #lim_{x to 0^-} e^(1/x) = e^(- oo) = 1/ e^( oo) = 0 #

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Answer 2

Scarlett Allison

To find the limit of e^(1/x) as x approaches 0^-, we can substitute a sequence of values approaching 0 from the left side into the function.

As x approaches 0 from the left side, the value of 1/x approaches negative infinity.

Using the limit properties, we can rewrite the expression as e^(1/x) = e^(-1/|x|) = 1/e^(1/|x|).

As x approaches 0 from the left side, |x| approaches 0, and thus 1/|x| approaches positive infinity.

Therefore, the limit of e^(1/x) as x approaches 0^- is 1/e^∞, which simplifies to 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.