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discont

find the discontinuities of a function (or generalized function) over the reals

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

discont(f, x )

Parameters

f

-

algebraic expression in x

x

-

name

Description

• 

discont returns a set of values where it is possible (not necessarily certain) that discontinuities occur.

• 

This function returns all the discontinuity points over the reals. This includes the points where the function goes to plus or minus infinity.

• 

Note that Dirac, though not a standard function, is considered to have a discontinuity when the argument is zero. This is because many algorithms in Maple treat all functions as pointwise defined, even if they are generalized functions.

• 

Multiple discontinuities may be expressed with the aid of extra variables with the names _Zn~, _NNn~, and _Bn~. When these variables appear in the answer, the expression f has discontinuities for all integer assignments to the variables _Zn~, for all non-negative integer assignments to the variables _NNn~, and for all binary assignments to the variables _Bn~.

Examples

discont1x,x

0

(1)

disconttanx,x

π_Z1~+12π

(2)

discontround3x12,x

13+13_Z2~

(3)

discontΓx2,x

2_NN1~

(4)

discontarctan1tan2x2x21,x

1,1,12π_Z3~+14π

(5)

discontDiracx1,x

1

(6)

f1sinx12

f:=1sinx12

(7)

discontf,x

16π+2π_Z4~,56π+2π_Z4~

(8)

Evaluating the function where it is discontinuous will result in an error.

fx=π6+2π1036π|fx=π6+2π1036π

Error, numeric exception: division by zero

See Also

fdiscont

iscont

limit

plot[options]

 


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