I tried to evaluate the limit <munder> <mo movablelimits="true" form="prefix">lim <mrow

Kaiden Wilkins

Kaiden Wilkins

Answered question

2022-05-12

I tried to evaluate the limit
lim x ln x 1 3 sin x

Answer & Explanation

Cortez Hughes

Cortez Hughes

Beginner2022-05-13Added 23 answers

Let f ( x ) = ln x 1 / 3 sin ( x ) . We have
lim inf x x π Z f ( x ) lim n f ( n π arcsin ( 1 / n ) ) = lim n ln ( n π arcsin ( 1 / n ) ) 1 / 3 1 / n =
and
lim sup x x π Z f ( x ) lim n f ( n π + arcsin ( 1 / n ) ) = lim n ln ( n π + arcsin ( 1 / n ) ) 1 / 3 1 / n = +
Hence f ( x ) has no limit when x , x π Z

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