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Eval help page

Alec Mihailovs 4475
August 09 2008
0

Eval help page contains the following statement:

Since eval does pointwise evaluation, eval cannot be used to evaluate an expression at a singularity. Use limit instead.

This is a serious error showing that the person writing it doesn't understand the difference between the value of a function at a point and the limit at that point.

At discontinuity, the value of a function is _not_ equal to the limit - that's why it is discontinuity. If the value of a function was equal to the limit, the function would be continuous at that point.

An example:

f:=piecewise(x=0,1,0);

                           { 1          x = 0
                      f := {
                           { 0        otherwise

eval(f,x=0);

                                  1

limit(f,x=0);

                                  0

x=0 is a discontinuity point. The value given by eval is correct, and evaluating it as limit is wrong.

Alec
example error

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