$$\lim_{x \to 0^-}\left(\frac{\tan{\left(5 \pi x \right)} \tan{\left(6 \pi x \right)}}{\sin{\left(2 \pi x \right)} \cos{\left(x i 8 \pi \right)} \sin{\left(3 \pi x \right)}}\right) = 5$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+}\left(\frac{\tan{\left(5 \pi x \right)} \tan{\left(6 \pi x \right)}}{\sin{\left(2 \pi x \right)} \cos{\left(x i 8 \pi \right)} \sin{\left(3 \pi x \right)}}\right) = 5$$
$$\lim_{x \to \infty}\left(\frac{\tan{\left(5 \pi x \right)} \tan{\left(6 \pi x \right)}}{\sin{\left(2 \pi x \right)} \cos{\left(x i 8 \pi \right)} \sin{\left(3 \pi x \right)}}\right) = 0$$
Más detalles con x→oo$$\lim_{x \to 1^-}\left(\frac{\tan{\left(5 \pi x \right)} \tan{\left(6 \pi x \right)}}{\sin{\left(2 \pi x \right)} \cos{\left(x i 8 \pi \right)} \sin{\left(3 \pi x \right)}}\right) = - \frac{10 e^{8 \pi}}{1 + e^{16 \pi}}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+}\left(\frac{\tan{\left(5 \pi x \right)} \tan{\left(6 \pi x \right)}}{\sin{\left(2 \pi x \right)} \cos{\left(x i 8 \pi \right)} \sin{\left(3 \pi x \right)}}\right) = - \frac{10 e^{8 \pi}}{1 + e^{16 \pi}}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty}\left(\frac{\tan{\left(5 \pi x \right)} \tan{\left(6 \pi x \right)}}{\sin{\left(2 \pi x \right)} \cos{\left(x i 8 \pi \right)} \sin{\left(3 \pi x \right)}}\right) = 0$$
Más detalles con x→-oo