AngouriMath
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TakeOutContinuousFactors(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom)
Method (no overloads)
Summary
The factors of expr that are continuous at a finite destination with a
finite non-zero value there, as that value, or that tend to a finite non-zero limit at an
infinite one, as that limit, and the product of the rest.
finite non-zero value there, as that value, or that tend to a finite non-zero limit at an
infinite one, as that limit, and the product of the rest.
Remarks
l'Hopital's rule differentiates both parts of the quotient, and a factor that tends to a
number other than 0 only makes the derivative larger: lim c(x) f(x) / g(x) is c(a) lim
f(x) / g(x). The product rule doubles it each time round, and with tanh written through
exponentials (1 - tanh(x)^2) * x * (1 + x^2) / tanh(x) at 0 from the right did not finish
in a minute, where x * (1 + x^2) / tanh(x) takes a tenth of a second. Only a factor real
for real x and with no step in it, so that its value at the point is its limit from
either side.
lim c(x) f(x) / g(x) is lim c(x) times lim f(x) / g(x) wherever the first is a finite
number other than 0. Left in, tanh(x) * x / (x + tanh(x)) at +oo did not finish in a
minute, and with it ln(x + tanh(x)) / ln(x), whose derivatives' quotient it is; taken
out, x / (x + tanh(x)) is 1.
number other than 0 only makes the derivative larger: lim c(x) f(x) / g(x) is c(a) lim
f(x) / g(x). The product rule doubles it each time round, and with tanh written through
exponentials (1 - tanh(x)^2) * x * (1 + x^2) / tanh(x) at 0 from the right did not finish
in a minute, where x * (1 + x^2) / tanh(x) takes a tenth of a second. Only a factor real
for real x and with no step in it, so that its value at the point is its limit from
either side.
lim c(x) f(x) / g(x) is lim c(x) times lim f(x) / g(x) wherever the first is a finite
number other than 0. Left in, tanh(x) * x / (x + tanh(x)) at +oo did not finish in a
minute, and with it ln(x + tanh(x)) / ln(x), whose derivatives' quotient it is; taken
out, x / (x + tanh(x)) is 1.
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