Cale Terrell
2022-10-22
Limits involving logarithm and argument in the complex plane
as
as
as
as
For the Log questions, I am getting for the first problem, then for the second I am getting only . Because the Log's in the questions are capitalized, I think I may have to add on to each of the answers. Is that correct?
for the last two problems (the Arg problems) I got zero for both because as n goes to infinity the n is the denominator for each so I thought they probably each go to zero. but also, the Arg is capitalized here as well, so I am getting the feeling I am doing these wrong. Can anybody help? Thanks!
Kaylee Evans
Beginner2022-10-23Added 20 answers
The meaning of capitalized names such as varies by source. I assume that has been defined so that it's continuous at and at ; this is the case for the common definitions I'm familiar with. Check your definition. Then
as
as
for all ; this is a constant sequence. Argument of a complex number is not affected by scaling.
since numerator does not depend on , while the denominator grows indefinitely.
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