I have to evaluate the following without L'Hopital's rule <munder> <mo movablelimits="tru

Jamison Rios 2022-07-01 Answered
I have to evaluate the following without L'Hopital's rule
lim x x tan ( 1 / x )
I can simplify this to be
lim x x sin ( 1 / x )
because
lim x cos ( 1 / x ) = 1
However, after that, I'm totally lost. L'Hopital's rule seems like my only option. Can someone help me out?
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Answers (1)

Elias Flores
Answered 2022-07-02 Author has 24 answers
If you are allowed to use the fact that lim t 0 sin ( t ) t = 1, then setting t = 1 x yields
lim x x sin ( 1 x ) = lim x sin ( 1 x ) 1 x = lim t 0 sin ( t ) t = 1
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