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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 this can include ranges in RealRange format.

• 

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+_Z2~3

(3)

discontGAMMAx2,x

2_NN1~

(4)

discontarctan1tan2x2x21,x

−1,1,12π_Z3~+14π

(5)

discontDiracx1,x

1

(6)

f1sinx12

f1sinx12

(7)

discontf,x

16π+2π_Z4~,56π+2π_Z4~

(8)

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

fx=Pi6+2Pi1036Pi|fx=Pi6+2Pi1036Pi

Error, numeric exception: division by zero

Example where a range is returned:

discontdilogy,y

0,0,

(9)

See Also

fdiscont

iscont

limit

plot[options]