Problem Set - Limits with Inverse Trigonometric Functions

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au
and

Department of Mathematics
University of Wisconsin, Madison
Madison, WI 53706 USA
ram@math.wisc.edu

Last updates: 7 December 2009

Limits with Inverse Trigonometric Functions

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

References [PLACEHOLDER]

[BG] A. Braverman and D. Gaitsgory, Crystals via the affine Grassmanian, Duke Math. J. 107 no. 3, (2001), 561-575; arXiv:math/9909077v2, MR1828302 (2002e:20083)