AngouriMath
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ArrivesOnTheCutOffTheRealLine(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity)
Method (no overloads)
Summary
Whether argument , a logarithm's or the base of a power, tends to
limit on the negative real line, where the logarithm has its cut, and
is not known to arrive there along the real line.
is not known to arrive there along the real line.
Remarks
The principal logarithm is continuous on its cut from above only. Its value there,
ln(-1) = i pi , is the limit along the line and from above, and from below the limit
is-i pi . So a limit read off a logarithm of an argument's limit is that limit only
where the argument does not come from below:x^x tends to -1 from below as x comes
down to -1, andlimitright(ln(x^x), x, -1) answered i pi . A power to an
exponent that is not whole ise^(exponent * ln(base)) and has the same cut. Which
side an argument off the real line comes from is not decided here, so a limit there is
declined, including one from above, whose answer was right.
#2266
is
where the argument does not come from below:
down to -1, and
exponent that is not whole is
side an argument off the real line comes from is not decided here, so a limit there is
declined, including one from above, whose answer was right.
#2266
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