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