Showing uniform convergence (or lack of) on [0,1]

dracond
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Homework Statement



Hello! I've been tasked with figuring out if the following is uniformly convergent on [0,1] and I could use push in the right direction:

sin(nx)


Homework Equations





The Attempt at a Solution



Would picking M=1 in the weierstrass-m test show it not uniformly convergent?
 
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Does it even converge pointwise?
 
Oops, it oscillates between [-1,1], no?
so does not converge pointwise.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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