Question

lim x->0 din arctg2x supra sin 3x
lim x->a din sinx-sina supra x-a
lim x->0 din sin3x+sin 5x supra x

DAU COROANA URGEEENT VA ROG

Answer 1

Răspuns

Explicație pas cu pas:

$1)\lim_{x \to 0} \frac{arctg(2x)}{sin(3x)}= \lim_{x \to 0} \frac{arctg(2x)}{2x}*\frac{3x}{sin(3x)}*\frac{2x}{3x}=1*1*\frac{2}{3}=\frac{2}{3}$

$2)\lim_{x \to a} \frac{sin(x)-sin(a)}{x-a}=f'(a)=cos(a), unde:f(x)=sin(x)$

$3)\lim_{x \to 0} \frac{sin(3x)+sin(5x)}{x}=\lim_{x \to 0} 3\frac{sin(3x)}{3x}+\lim_{x \to 0} 5\frac{sin(5x)}{5x}=3*1+5*1=8$