Input & Output Tolerances for a Linear Function
by Mike Martin

On this page, you can examine what input tolerance tolerance, δ, is necessary for a given output tolerance, ε We examine this only for a linear function of the form

f(x) = m x + b

More specifically, we discuss the input and output tolerances for this function in the context of the limit of f ( x ) as xc. The user inputs the values of m, b, c, and ε In addition, the user inputs the minimum & maximum x-values for plotting, xmin and xmax, respectively. Note that the results are not meaningful when m = 0. A graph is generated to visualize this and a value for δ is calculated. If the input, therefore, is within δ units of c, then the output is within ε units of f ( c ).

Enter in the value of the parameter a and select the plotting bounds, then press the "Plot/Evaluate" button.

m =  

b =  

c =  

ε =  

  ≤   x   ≤  


Wikipedia's Limit of a Function

MathWorld's Epsilon-Delta Definition

MathWorld's Epsilon-Delta Proof