AngouriMath
DivergesAtAVanishingDivisor(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom)
Method (no overloads)
Summary
The infinity a quotient tends to when its divisor vanishes and its dividend does not,
ornull where that is not the shape or the side the divisor
vanishes from cannot be read off.
or
vanishes from cannot be read off.
Remarks
The descent puts each part's own limit in place of the part, and for this shape that
throws away the only thing that decides the answer.cos(x) / sin(x) at 0
becomes1 / 0 , which is NaN -- the claim that the limit does not exist -- where
on the right it is +oo and on the left -oo.
vanish with it. Whereg(a) = 0 and the first non-vanishing derivative there is
the k-th,g(x) has the sign of g_k(a) * (x - a)^k near a, which is the
sign ofg_k(a) on the right and that times (-1)^k on the left. Nothing
is claimed unless a derivative comes out finite and non-zero at the point: an
expression that is not differentiable there, or whose derivative diverges as
sqrt(x) 's does, is left alone.
throws away the only thing that decides the answer.
becomes
on the right it is +oo and on the left -oo.
vanish with it. Where
the k-th,
sign of
is claimed unless a derivative comes out finite and non-zero at the point: an
expression that is not differentiable there, or whose derivative diverges as
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