Evaluate the limit lim_(x -> 0)(-zx ln (zx))/(-x ln x)

Mattie Monroe

Mattie Monroe

Answered question

2022-10-16

Evaluate the limit lim x 0 z x ln ( z x ) x ln x
Title says it all. How can I evaluate the limit provided as:
lim x 0 + z x ln ( z x ) x ln x
I do know that it is equal to z. What I do not know is why.

Answer & Explanation

Cagliusov8

Cagliusov8

Beginner2022-10-17Added 15 answers

lim x 0 + z x ln ( z x ) x ln x = z lim x 0 + ln ( z x ) ln x = z lim x 0 + z z x 1 x = z
omgespit9q

omgespit9q

Beginner2022-10-18Added 3 answers

HINT:
z x log ( z x ) x log x = z log z + log x log x = z [ log z log x + 1 ]

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?