AngouriMath
AsQuotientOfVanishingAndDiverging(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom)
Method (no overloads)
Summary
A product of something vanishing with something diverging, written as the quotient
of the diverging factor by the reciprocal of the vanishing one, or
null where it is not that shape.
of the diverging factor by the reciprocal of the vanishing one, or
Remarks
This is the other way a product can be indeterminate without being written as a
quotient, and the split above cannot see it:sin(x) * ln(x) has no reciprocal
factor at all, so both halves go into the numerator and it comes back unchanged.
the other way round, though both give an indeterminate quotient. Differentiating
ln(x) / csc(x) gets rid of the logarithm and arrives at an answer; the other
arrangement,sin(x) / (1 / ln(x)) , differentiates into a product of the same
shape as the one it started from and goes round.
quotient, and the split above cannot see it:
factor at all, so both halves go into the numerator and it comes back unchanged.
the other way round, though both give an indeterminate quotient. Differentiating
arrangement,
shape as the one it started from and goes round.
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