$\lim_{x\to \infty}\arcsin\frac{1-x}{1+x}$

Question

$$\lim_{x\to \infty}\arcsin\frac{1-x}{1+x}$$

using $\lim_{x\to0}\frac{\arcsin}{x}=1$, using a change the variable like $t=\frac{1}{x}$, did't help

Answer 1

using the continuity of arcsin, I think you can say that your limit is equal to

$$\arcsin \left(\lim_{x\to\infty} \frac{1-x}{1+x}\right)$$

Answer 2

Find the limit of $\frac{1-x}{1+x}$ when $x \to\infty $