Используя замечательный предел
0} \frac{sin (5x)}{x}=lim_{x->0} \frac{sin (5x)}{5x}*5=\\\\5*lim_{5x->0} \frac{sin (5x)}{5x}=|5x=t|=5*lim_{t->0}\frac{sin t}{t}=5*1=5" alt="lim_{x->0} \frac{sin (5x)}{x}=lim_{x->0} \frac{sin (5x)}{5x}*5=\\\\5*lim_{5x->0} \frac{sin (5x)}{5x}=|5x=t|=5*lim_{t->0}\frac{sin t}{t}=5*1=5" align="absmiddle" class="latex-formula">