Limit of the sine and logarithm function How do I calculate the following? lim_(x -> 0^(+)) (-ln(x) sin(x))

Jairo Hodges

Jairo Hodges

Answered question

2022-11-11

Limit of the sine and logarithm function
How do I calculate the following?
lim x 0 + ( ln ( x ) sin ( x ) )

Answer & Explanation

ebizsavvy1txn

ebizsavvy1txn

Beginner2022-11-12Added 14 answers

lim x 0 + ( ln ( x ) sin ( x ) ) = lim x 0 + ( x ln ( x ) sin x x )
This is equal to
( lim x 0 + x ln ( x ) ) ( lim x 0 + sin x x )
provided those both exist.
The first of those can be found by writing lim x 0 + ln x 1 / x and applying L'Hopital's rule.
atgnybo4fq

atgnybo4fq

Beginner2022-11-13Added 5 answers

Do you recognize this limit as having a certain indeterminate form? Identify this form, and apply the standard technique from your textbook in order to deal with it. In case you don't have a textbook, this is 0 type. Rearrange the expression ln ( x ) sin ( x ) to be 0 0 form or form. Then use L'Hospital's Rule.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?