Problem Set - Limits with Inverse Trigonometric Functions

## Problem Set - Limits with Inverse Trigonometric Functions

 Evaluate $\underset{x\to 1}{lim}\frac{1-x}{{\mathrm{arccos}}^{2}x}$. Evaluate $\underset{x\to 1/\sqrt{2}}{lim}\frac{x-\mathrm{cos}\left(\mathrm{arcsin}x\right)}{1-\mathrm{tan}\left(\mathrm{arcsin}x\right)}$. Evaluate $\underset{x\to 0}{lim}\frac{x\left(1-\sqrt{1-{x}^{2}}\right)}{{\mathrm{arcsin}}^{3}\left(x\right)\sqrt{1-{x}^{2}}}$. Evaluate $\underset{x\to 1}{lim}\frac{1-x}{\pi -2\mathrm{arcsin}x}$. Evaluate $\underset{x\to 1}{lim}\frac{\mathrm{arctan}2x}{\mathrm{sin}3x}$.