How do I evaluate the limit given ? \lim_{x\to\infty}\frac{x^x-(x-1)^x}{x^x}

veleumnihryz 2022-04-25 Answered
How do I evaluate the limit given ?
limxxx(x1)xxx
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Answers (1)

kayuukor9c
Answered 2022-04-26 Author has 13 answers
Then
limxxx(x1)xxx=limx[1(x1x)x]=limx[1(11x)x]
Notice
limx(11x)x=elimxxln(11x)
Try making a substitution like u=1x to get a situation in which l'Hôpital's rule applies to find this limit. Remember this will also change the value the limit approaches. It should look something like this:
elimu0ln(1u)u=elimu01u1
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