I know the value of the limit is &#x2212;<!-- - --> <mstyle displaystyle="true" scriptlevel="0"

civilnogwu

civilnogwu

Answered question

2022-07-05

I know the value of the limit is 1 6 . I tried to use the fact
ln ( a b ) = ln ( a ) + ln ( b )

Answer & Explanation

kawiarkahh

kawiarkahh

Beginner2022-07-06Added 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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