$$\lim_{x \to 0^-} \operatorname{asin}{\left(3 x \right)} = 0$$
More at x→0 from the left$$\lim_{x \to 0^+} \operatorname{asin}{\left(3 x \right)} = 0$$
$$\lim_{x \to \infty} \operatorname{asin}{\left(3 x \right)} = - \infty i$$
More at x→oo$$\lim_{x \to 1^-} \operatorname{asin}{\left(3 x \right)} = \operatorname{asin}{\left(3 \right)}$$
More at x→1 from the left$$\lim_{x \to 1^+} \operatorname{asin}{\left(3 x \right)} = \operatorname{asin}{\left(3 \right)}$$
More at x→1 from the right$$\lim_{x \to -\infty} \operatorname{asin}{\left(3 x \right)} = \infty i$$
More at x→-oo