What is the correct solution for the limit <munder> <mo movablelimits="true" form="prefix">

Kiana Dodson 2022-06-30 Answered
What is the correct solution for the limit lim x x sin 1 x ?
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Answers (2)

Turynka2f
Answered 2022-07-01 Author has 17 answers
lim x x sin 1 x = lim x sin ( 1 x ) 1 x = lim u 0 sin ( u ) u = 1
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Garrett Black
Answered 2022-07-02 Author has 5 answers
The first line of reasoning is clearly incorrect: let f(x)=x, g ( x ) = ( x 2 + 1 ) 1 . Then
lim x f ( x ) =
and g ( x ) ( 0 , 1 ] is clearly bounded on R . But
lim x f ( x ) g ( x ) = lim x 1 x + 1 / x = 0.
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