Răspuns
Explicație pas cu pas:
[tex]1)\lim_{x \to 0} \frac{arctg(2x)}{sin(3x)}= \lim_{x \to 0} \frac{arctg(2x)}{2x}*\frac{3x}{sin(3x)}*\frac{2x}{3x}=1*1*\frac{2}{3}=\frac{2}{3}[/tex]
[tex]2)\lim_{x \to a} \frac{sin(x)-sin(a)}{x-a}=f'(a)=cos(a), unde:f(x)=sin(x)[/tex]
[tex]3)\lim_{x \to 0} \frac{sin(3x)+sin(5x)}{x}=\lim_{x \to 0} 3\frac{sin(3x)}{3x}+\lim_{x \to 0} 5\frac{sin(5x)}{5x}=3*1+5*1=8[/tex]
