$$\lim_{x \to 0^-}\left(\log{\left(\cos^{6}{\left(x \right)} \right)} \operatorname{asin}{\left(2 \sqrt{x} \right)}\right) = 0$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+}\left(\log{\left(\cos^{6}{\left(x \right)} \right)} \operatorname{asin}{\left(2 \sqrt{x} \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\log{\left(\cos^{6}{\left(x \right)} \right)} \operatorname{asin}{\left(2 \sqrt{x} \right)}\right) = - \infty i \log{\left(\left\langle 0, 1\right\rangle \right)}$$
Más detalles con x→oo$$\lim_{x \to 1^-}\left(\log{\left(\cos^{6}{\left(x \right)} \right)} \operatorname{asin}{\left(2 \sqrt{x} \right)}\right) = 6 \log{\left(\cos{\left(1 \right)} \right)} \operatorname{asin}{\left(2 \right)}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+}\left(\log{\left(\cos^{6}{\left(x \right)} \right)} \operatorname{asin}{\left(2 \sqrt{x} \right)}\right) = 6 \log{\left(\cos{\left(1 \right)} \right)} \operatorname{asin}{\left(2 \right)}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty}\left(\log{\left(\cos^{6}{\left(x \right)} \right)} \operatorname{asin}{\left(2 \sqrt{x} \right)}\right) = \infty i \log{\left(\left\langle 0, 1\right\rangle \right)}$$
Más detalles con x→-oo