Źródło TeX:

\underset{x\rightarrow 0^{+}}{\lim }\,\dfrac{\ln (\sin x )}{\ln ^{2}{x}}=\left[ \dfrac{-\infty }{\infty }\right] \overset{\text{H}}{=}\underset{x\rightarrow 0^{+}}{\lim }\,\dfrac{\frac{1}{\sin x}\cdot \cos x}{2\ln x \cdot \frac{1}{x}}=\underset{x\rightarrow 0^{+}}{\lim }\,\dfrac{x}{\sin x} \cdot \dfrac{\cos x}{2\ln x}=\left[ 1\cdot\dfrac{1}{-\infty}\right] =0