Limit

Author

Eric W. Weisstein
June 21, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/Limit.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Limit.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Notation

Limit[f[x],x->0]//TraditionalForm

Limit[f[x],x->0,Direction->-1]//TraditionalForm

Limit[f[x],x->0,Direction->1]//TraditionalForm

Definition

Limit[(f[x+ε]-f[x])/ε,ε->0]

Limit[(f[x+ε]-f[x])/ε,ε->0,Analytic->True]

Limit[(f[x+ε]-f[x-ε])/(2ε),ε->0]

Limit[(f[x+ε]-f[x-ε])/(2ε),ε->0,Analytic->True]

Special Cases

Limit[Sin[1/x],x->0]

Limit[x Sin[1/x],x->0]

FoxTrot Limit

Plot[((Sqrt[(x^3)-(x^2)+3x])/((Sqrt[(x^3)])-(Sqrt[(x^2)])+(Sqrt[3x]))),{x,.1,100},PlotStyle->Red,PlotRange->{.95,1.14}]

Limit[((Sqrt[(x^3)-(x^2)+3x])/((Sqrt[(x^3)])-(Sqrt[(x^2)])+(Sqrt[3x]))),x->∞]