Problem Set - Evaluating Limits when $x\to \infty$

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

Evaluating Limits when $x\to \infty$

	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{x+2}{x-2}}$.
	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{3x^2+2x-5}{5x^2+3x+1}}$.
	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{x^2-7x+11}{3x^2+10}}$.
	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{2x^3-5x+7}{7x^3+x^2-6}}$.
	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{2x^3-5x+7}{7x^3+x^2-6}}$.
	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{\left(3x-1\right)\left(4x-5\right)}{\left(x-6\right)\left(x-3\right)}}$.
	Evaluate ${\displaystyle \underset{n\to \infty }{lim}\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\dots +\frac{1}{3^n}\right)}$.
	Evaluate ${\displaystyle \underset{x\to \infty }{lim}\frac{x}{\sqrt{4x^2-1}-1}}$.
	Evaluate ${\displaystyle \underset{x\to -\infty }{lim}{2}^x}$.
	Evaluate ${\displaystyle \underset{n\to \infty }{lim}{\left(1+\frac{1}{n}\right)}^n}$.
	Evaluate ${\displaystyle \underset{t\to \infty }{lim}\frac{t+1}{t^2+1}}$.
	Evaluate ${\displaystyle \underset{n\to \infty }{lim}\sqrt{n^2+1}+n}$.
	Evaluate ${\displaystyle \underset{n\to \infty }{lim}\sqrt{n^2+n}+n}$.

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)