Thanks Ivana. The solution of the limit can be evaluated by considering that f (x) = x goes to infinity much faster than f (x) = lnx. The denominator goes to infinity faster than the numerator and therefore their ratio tends to 0.
Thank you for explanations. I wonder if soon there is gonna be something related to partial differential equations, I would like to refresh my knowledge :D
Great video and explanation. When we put the limit inside to evaluate the other function, does the outer function have to be continuous on all real numbers? Or is it ok even if it is a small interval from (a,b) as long as it's continuous there? Because ln(x)/x is defined from (0,∞) and not R.
Very good question, thank you. So 1. we have to find the limit of the function g(x) which Is in our case ln(x)/x as x goes to infinity. We get it's 0 and then if the limit exists the function f must be continuous at exactly that point.
@@intellecta2686 Thanks for your help, Ivana. Sometimes I get confused by this continuity. Understanding these concepts and properties really helped me excel in my calc courses.
