AngouriMath
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LogarithmDiverges(AngouriMath.Entity)
Method (no overloads)
Summary
Whether the logarithm of something tending to argumentLimit diverges, which is where the argument tends to zero or to an infinity.
Remarks
Read off the value wherever the limit has one, and off its form only where it does
not. A limit comes back in whatever form the reading that found it left it in, and
the substitution leaves the expression with +oo put in for x: cos(1/x) tends to
cos(1 / +oo) , which has an infinity in it and is 1. Read off the form, its
logarithm diverged, so ln(x) / ln(cos(x)) at 0+ -- -oo over a divisor vanishing from
below, which is +oo -- was taken for oo/oo and differentiated into
(1/x) / (-tan(x)), and answered -oo. l'Hopital's rule says nothing about a quotient
whose divisor vanishes and whose dividend does not.
https://github.com/asc-community/AngouriMath/issues/2267
+oo * a , or an infinity with an
imaginary part -- is still read off its form.
not. A limit comes back in whatever form the reading that found it left it in, and
the substitution leaves the expression with +oo put in for x: cos(1/x) tends to
logarithm diverged, so ln(x) / ln(cos(x)) at 0+ -- -oo over a divisor vanishing from
below, which is +oo -- was taken for oo/oo and differentiated into
(1/x) / (-tan(x)), and answered -oo. l'Hopital's rule says nothing about a quotient
whose divisor vanishes and whose dividend does not.
https://github.com/asc-community/AngouriMath/issues/2267
imaginary part -- is still read off its form.
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