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How do you determine the limit of # e^x/(x-5)^3# as x approaches #5^+#?

Answer 1

Charles Arocha

#=oo#

#lim_(x->5^+) (e^x)/(x-5)^3#

#=e^5/0#

#=oo#

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Answer 2

William Abdalla

To determine the limit of e^x/(x-5)^3 as x approaches 5^+, we can use L'Hôpital's Rule. Taking the derivative of both the numerator and denominator, we get (e^x)/(3(x-5)^2). Plugging in x=5, we find that the limit is e^5/0, which is undefined.

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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.

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