$$\lim_{x \to 0^-} \left(\frac{\operatorname{asin}^{2}{\left(x \right)}}{\sin{\left(5 x \right)} \tan{\left(3 x \right)}}\right)^{\frac{1}{x}} = 0$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+} \left(\frac{\operatorname{asin}^{2}{\left(x \right)}}{\sin{\left(5 x \right)} \tan{\left(3 x \right)}}\right)^{\frac{1}{x}} = 0$$
$$\lim_{x \to \infty} \left(\frac{\operatorname{asin}^{2}{\left(x \right)}}{\sin{\left(5 x \right)} \tan{\left(3 x \right)}}\right)^{\frac{1}{x}}$$
Más detalles con x→oo$$\lim_{x \to 1^-} \left(\frac{\operatorname{asin}^{2}{\left(x \right)}}{\sin{\left(5 x \right)} \tan{\left(3 x \right)}}\right)^{\frac{1}{x}} = \frac{\pi^{2}}{4 \sin{\left(5 \right)} \tan{\left(3 \right)}}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+} \left(\frac{\operatorname{asin}^{2}{\left(x \right)}}{\sin{\left(5 x \right)} \tan{\left(3 x \right)}}\right)^{\frac{1}{x}} = \frac{\pi^{2}}{4 \sin{\left(5 \right)} \tan{\left(3 \right)}}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty} \left(\frac{\operatorname{asin}^{2}{\left(x \right)}}{\sin{\left(5 x \right)} \tan{\left(3 x \right)}}\right)^{\frac{1}{x}}$$
Más detalles con x→-oo