I have to check the uniform convergence of the below mentioned function sequence: $f_n(x) = \frac{1-\ln x}{nx}$ while $0<x<1$
at the answers, it's told that the sequence doesn't converge uniformly - but somehow I receive that it does uniformly converge.
I looked for the maximum of the function and received the max point equals $e^2$. when I look for the value of $\lim_{n\to \infty} f_n(e^2)$ , it equals 0 - meaning it does converge. (in cotradiction to the answers)
what am I doing wrong? thanks.