Recent content by penroseandpaper

I came across this question on chegg for practice as I'm self learning complex analysis, but became stumped on it and without access to the solution am unable to check. Let $$ f(z)=\frac{cos(z)} {(z-π/2)^7} $$. Then the singularity is at π/2. And on first appearance, it looks like a pole of...

Hi everyone, We've been looking at Fourier series and related topics in online class, touching upon odd and even periodic extensions. However, we haven't looked at what this translates to for sine and cosine functions - only sawtooth and line examples. So, I'm trying to do my own investigation...

Hi all, I've been trying to follow a question I came across on a website. And I'm able to understand everything up until the separation of variables for solving the differential equation and coming to a solution with arctan. But there are a few things that aren't explained that I was hoping...

Here's corrected question 1

Would somebody be kind enough to check whether I've picked the right convergence tests for each of these and reached the right answers? There are no solutions in the book. Also, is there a method I can use to determine if I'm right - does calculating the first n terms help? Thank you Edit...

Ah, thanks for clarifying. So, it's converging. Is there any other more appropriate/simpler way of showing it's converging other than either rewriting over common denominator and dividing through by the dominant term - just wondering if I'm missing something more obvious? Thanks

A sequence is made up of two sequences an=(n^2)/(n+2) - (n^2)/(n+3) The problem asks for the solver to work out if it's converging or diverging, and find a limit if possible. My first thought was to write both over a common denominator and then divide through by the dominant term; this...

If I'm given a set of four vectors, such as A={(0,1,4,2),(1,0,0,1)...} and am given another set B, whose vectors are given as a form such as (x, y, z, x+y-z) all in ℝ, what steps are needed to show A is a basis of B? I have calculated another basis of B, and found I can use linear combinations...

Hi, The textbook asks me to use subgroup axioms to prove why a set of permutations that interchange two specific symbols in S4 is or isn't a subgroup of the symmetric group, and the same for a set of permutations that fix two elements. My guess is that the set of permutations that interchange...

Thanks for pointing that out. Please find corrected solution below (hopefully...). So it's not associative as the two expressions aren't equal. Before I go in search of something that doesn't exist, is there an identity element for an operation like this?

I simplified the operation but maybe I shouldn't have.

But isn't the fact you won't find one that does both the reason this binary operation doesn't have an identity element? Because a•e=(a+e)/(ae); if e=0 it's undefined and if e=1 it no longer equals a. Apologies if I'm wrong - I was fine when the operations were just addition, subtraction...

My apologies, I thought I'd included a star after ℝ for ℝ*. As for the associativity, you might be right; if I'm correct (big if) a•(b•c)=c+b+1/a (a•b)•c=b+a+1/c

Hi everyone, I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track. If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...

Hi everyone, We've just started special relativity and I'm just wondering if you'd mind clarifying something for me. The transformation is described as x'=x-vt, where x' is moving relative to x. However, in the diagram I've attached, x' is ahead of x ; so why is the transformation described...