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civilnogwu 2022-07-05 Answered
I know the value of the limit is 1 6 . I tried to use the fact
ln ( a b ) = ln ( a ) + ln ( b )
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Answers (1)

kawiarkahh
Answered 2022-07-06 Author has 15 answers
We use
lim y 0 ln ( y + 1 ) y = 1
Letting y = n sin 1 n 1 so
n 2 ln ( n sin 1 n ) = n 2 ( n sin 1 n 1 ) ln ( n sin 1 n ) n sin 1 n 1
so the limit is replaced by
lim n n 2 ( n sin 1 n 1 )
and as remarked this is an application of
lim x 0 sin x x x 3
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