[tex] \lim_{x\to 0} sin(3x) ctg (5x)= \lim_{x\to 0} sin(3x) \cdot \frac{cos(5x)}{sin(5x)}= \lim_{x\to 0} \frac{sin (3x) cos(5x)}{sin(5x)}=[/tex]
Reguła de l'Hospitala
[tex] \lim_{x\to 0} \frac{cos (3x) \cdot3-sin(5x)\cdot 5}{cos 5(x)\cdot5}= \lim_{x\to 0} \frac{3cos (3x)-5sin(5x)}{5cos 5(x)}=\frac{3\cdot1-5\cdot0}{5\cdot1}=\frac{3}{5}[/tex]
