how to prove that lim(1/ln x)=0 if x ? 8 step by step based on definition l f(x)-0l<e

Question

how to prove that lim(1/ln x)=0 if x → ∞ step by step based on definition l f(x)-0l<ε

Answer 1

What you want to show is that for every ε>0 there exists a number k such that when x>k then |1/ln(x) - 0| <ε.

 

Since x goes to infinity without loss of generality we can remove the absolute value sign.

 

We want to show (1/ln(x)) < ε for x > k.

 

This gives 1/ε < ln(x). Solve for x and you are one step away from being done.

 

 

Let me know if you have any questions.