$$\lim_{x \to 0^-}\left(\frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}\right) = \frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}\right) = \frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}$$
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}\right) = \frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}$$
Más detalles con x→oo$$\lim_{x \to 1^-}\left(\frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}\right) = \frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+}\left(\frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}\right) = \frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}\right) = \frac{\sin^{2}{\left(4 \right)}}{\sin^{2}{\left(8 \right)}}$$
Más detalles con x→-oo