(C) Copyright 1994 D.C.M. Burbulla and  C.T.J. Dodson
       Notebook to support the book
     Self-Tutor for Computer  Calculus

Using Mathematica 2

by
     D. C. M. Burbulla and C. T. J. Dodson, University of Toronto
 Published by:    
    Prentice-Hall Canada  (English)   ISBN 0130152803     and 
     Prentice-Hall Japan  (Japanese) ISBN4-8101-8558-3 C3055 P2880E

Beginning Calculus

Here we illustrate the epsilon-delta test for continuity using some new functions.

Chap2.m

epsilondeltatest/:
        epsilondeltatest[f_, {a_, d_}, {l_, e_}] :=
        Block[{x}, Plot[f[x], {x, a - d, a + d}, 
	PlotRange -> {{a - d, a + d}, {l - e, l + e}},
	Frame -> True]]

epsilondeltatest::usage = "epsilondeltatest[f, {a, d}, {l, e}] plots a graph of f
 on the interval {a - d, a + d} to see if |f[x] - l| < e for all x such that 
 |x - a| < d."


repsilondeltatest/:
        repsilondeltatest[f_, {a_, d_}, {l_, e_}] :=
        Block[{x}, Plot[f[x], {x, a, a + d}, 
	PlotRange -> {{a, a + d},{l - e, l + e}},
	Frame -> True]]

repsilondeltatest::usage = "repsilondeltatest[f, {a, d}, {l, e}] plots a grahp of f
 on the interval {a, a + d} to see if |f[x] - l| < e for all x such that 0 < x - a < d."


lepsilondeltatest/:
        lepsilondeltatest[f_, {a_, d_}, {l_, e_}] :=
        Block[{x}, Plot[f[x], {x, a - d, a}, 
	PlotRange -> {{a - d, a}, {l - e, l + e}},
	Frame -> True]]

lepsilondeltatest::usage = "lepsilondeltatest[f, {a, d}, {l, e}] plots a graph of f
 on the interval {a - d, a} to see if |f[x] - l| < e for all x such that 0 < a - x < d."

Example 1

Clear[f]; f[x_]:= x Sin[1/x]

epsilondeltatest[f, {0,0.1}, {0,0.1}];

epsilondeltatest[f, {0,0.1}, {0,0.01}];

repsilondeltatest[f, {0,0.1}, {0,0.1}];