$$\lim_{x \to 0^-} \operatorname{asin}{\left(\frac{\cos{\left(x \right)} - \cos{\left(\sin{\left(2 x \right)} \right)}}{x^{2}} \right)} = \operatorname{asin}{\left(\frac{3}{2} \right)}$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+} \operatorname{asin}{\left(\frac{\cos{\left(x \right)} - \cos{\left(\sin{\left(2 x \right)} \right)}}{x^{2}} \right)} = \operatorname{asin}{\left(\frac{3}{2} \right)}$$
$$\lim_{x \to \infty} \operatorname{asin}{\left(\frac{\cos{\left(x \right)} - \cos{\left(\sin{\left(2 x \right)} \right)}}{x^{2}} \right)} = 0$$
Más detalles con x→oo$$\lim_{x \to 1^-} \operatorname{asin}{\left(\frac{\cos{\left(x \right)} - \cos{\left(\sin{\left(2 x \right)} \right)}}{x^{2}} \right)} = \operatorname{asin}{\left(- \cos{\left(\sin{\left(2 \right)} \right)} + \cos{\left(1 \right)} \right)}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+} \operatorname{asin}{\left(\frac{\cos{\left(x \right)} - \cos{\left(\sin{\left(2 x \right)} \right)}}{x^{2}} \right)} = \operatorname{asin}{\left(- \cos{\left(\sin{\left(2 \right)} \right)} + \cos{\left(1 \right)} \right)}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty} \operatorname{asin}{\left(\frac{\cos{\left(x \right)} - \cos{\left(\sin{\left(2 x \right)} \right)}}{x^{2}} \right)} = 0$$
Más detalles con x→-oo