Applicare la formula: $\frac{a}{\frac{b}{c}}$$=\frac{ac}{b}$, dove $a=\ln\left(x\right)\cos\left(\frac{1}{x}\right)$, $b=1$, $c=x$, $a/b/c=\frac{\ln\left(x\right)\cos\left(\frac{1}{x}\right)}{\frac{1}{x}}$ e $b/c=\frac{1}{x}$

Applicare la formula: $\lim_{x\to c}\left(a\right)$=indeterminate, dove $a=x\ln\left(x\right)\cos\left(\frac{1}{x}\right)$, $c=\infty $ e $x->c=x\to\infty $