(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to show that [itex]f_{n}[/itex]=sin([itex]\frac{z}{n}[/itex]) converges uniformly to 0.

2. Relevant equations

So I need to find K([itex]\epsilon[/itex]) such that [itex]\forall[/itex][itex]n \geq K[/itex]

|sin([itex]\frac{z}{n}[/itex])|<[itex]\epsilon[/itex]

I'm trying to prove this in an annulus: [itex]\alpha\leq |z| \leq\beta[/itex]

3. The attempt at a solution

I'm having trouble because no matter what I choose for K I can't get the epsilon to come out.

I'm trying something like K([itex]\epsilon[/itex])=[itex]\frac{1}{\alpha\epsilon}[/itex].

My problem is that I can't say that sin([itex]\frac{z}{n}[/itex])<sin([itex]\frac{\alpha}{n}[/itex])

Which is how I've been doing these uniform convergence ones (recasting in terms of [itex]\alpha[/itex] instead of z).

Anyways I was hoping I could get some help on how to proceed.

Thanks!

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# Homework Help: Uniform convergence

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