$$\lim_{x \to \infty}\left(\frac{\sin{\left(5 \pi x \right)} \operatorname{asin}{\left(x - 1 \right)}}{\left(- 2 x + \left(x^{2} + 1\right)\right) \operatorname{acos}{\left(x - 1 \right)}}\right) = \left\langle -1, 1\right\rangle \lim_{x \to 0^+}\left(- \frac{x^{2} \operatorname{asin}{\left(1 - \frac{1}{x} \right)}}{x^{2} \operatorname{acos}{\left(-1 + \frac{1}{x} \right)} - 2 x \operatorname{acos}{\left(-1 + \frac{1}{x} \right)} + \operatorname{acos}{\left(-1 + \frac{1}{x} \right)}}\right)$$
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(5 \pi x \right)} \operatorname{asin}{\left(x - 1 \right)}}{\left(- 2 x + \left(x^{2} + 1\right)\right) \operatorname{acos}{\left(x - 1 \right)}}\right) = 0$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+}\left(\frac{\sin{\left(5 \pi x \right)} \operatorname{asin}{\left(x - 1 \right)}}{\left(- 2 x + \left(x^{2} + 1\right)\right) \operatorname{acos}{\left(x - 1 \right)}}\right) = 0$$
Más detalles con x→0 a la derecha$$\lim_{x \to 1^-}\left(\frac{\sin{\left(5 \pi x \right)} \operatorname{asin}{\left(x - 1 \right)}}{\left(- 2 x + \left(x^{2} + 1\right)\right) \operatorname{acos}{\left(x - 1 \right)}}\right) = -10$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+}\left(\frac{\sin{\left(5 \pi x \right)} \operatorname{asin}{\left(x - 1 \right)}}{\left(- 2 x + \left(x^{2} + 1\right)\right) \operatorname{acos}{\left(x - 1 \right)}}\right) = -10$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty}\left(\frac{\sin{\left(5 \pi x \right)} \operatorname{asin}{\left(x - 1 \right)}}{\left(- 2 x + \left(x^{2} + 1\right)\right) \operatorname{acos}{\left(x - 1 \right)}}\right) = \left\langle -1, 1\right\rangle \lim_{x \to 0^-}\left(- \frac{x^{2} \operatorname{asin}{\left(1 - \frac{1}{x} \right)}}{x^{2} \operatorname{acos}{\left(-1 + \frac{1}{x} \right)} - 2 x \operatorname{acos}{\left(-1 + \frac{1}{x} \right)} + \operatorname{acos}{\left(-1 + \frac{1}{x} \right)}}\right)$$
Más detalles con x→-oo