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[CAS] limit() question - DrD - 05-25-2018 10:27 AM
I encountered this limit example:
limit(ABS((x-2)^(n+1)/((n+1)^2*3^(n+1)) / ((x-2)^n/(n^2*3^n))),n,∞); ==> undef
During a simplification process, (of the underlying expression), a result is obtained at this equivalent expression:
limit(ABS((x-2)*n^2/((n+1)^2*3)),n,∞); ==> ABS(x-2)/3
Further simplification continues to return ABS(x-2)/3. Should the original (un-simplified) expression, also return this result, (instead of "undef")?
-Dale-
RE: [CAS] limit() question - parisse - 05-26-2018 06:07 AM
Yes, undef is expected, because limit does series expansion without simplifications (because simplify could return a much harder limit), and you can not do that for (x-2)^n without assumption on x (need to know the sign of ln(x-2)). If you run for example assume(x>3) the initial limit will be solved. Or if you run simplify, because it will remove the (x-2)^n.
RE: [CAS] limit() question - DrD - 05-26-2018 08:19 AM
Thank you for your explanation, Parisse.
-Dale-