Problem Set - Limits with 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 Trigonometric Functions

	Evaluate limx→0sin3x4x.
	Evaluate limx→0sinxcosx3x.
	Evaluate limx→0tanxx.
	Evaluate limx→01-cosxsin2x.
	Evaluate limx→0tanaxtanbx.
	Evaluate limx→0sinx/4x.
	Evaluate limx→0sinmxtannx.
	Evaluate limθ→01-cos6θθ.
	Evaluate limx→01-cos2x3tan2x.
	Evaluate limx→0cos2x1-sinx.
	Evaluate limx→0tan2x-x3x-sinx.
	Evaluate limx→asinx-sinax-a.
	Evaluate limx→0sin5x-sin3xsinx.
	Evaluate limx→0tan3x-2x3x-sin2x.
	Evaluate limx→0x2-tan2xtanx.
	Evaluate limx→π/41-tanxx-π/4.
	Evaluate limx→0tanx/23x.
	Evaluate limx→01-cos2x+tan2xxsinx.
	Show that if limx→0kxcscx=limx→0xcsckx, then k=±1.
	Evaluate limh→0sina+h-sinah.
	Evaluate limh→∞cosπ/hh-2.

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)