How to prove that f(x) = x^epsilon - log x is oo when x-> oo?

rochioblogmz

rochioblogmz

Answered question

2022-10-29

How to prove that f ( x ) = x ε log x is when x ?
I'm trying to prove that the function x ε is "bigger" than log x when x , for every ε > 0
Or to put it in a more formal way:
For every ε > 0, there exists a constant N for which all x > N the following is true:
x ε > log x
I don't believe that the base of the log is important for this one, but just in case, it is 2.

Answer & Explanation

blogpolisft

blogpolisft

Beginner2022-10-30Added 10 answers

hint: Show x ϵ log x + by L'hospitale rule.

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