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Okay, I have this function defined as an infinite series:

which is converges uniformly and absolutely for x > 0. I have shown that f is continous and has a derivative for x > 0. Now I have to show that [tex]f(x) \rightarrow 0[/tex] as [tex]x \rightarrow \infty.[/tex] It's obvious that it is the case, but how do I prove it. I've tried putting 1/x outside the sum, but then I don't know about the remaining part. Any ideas?

[tex]f(x) = \sum_{n=1}^{\infty}\frac{\sin(nx)}{x+n^4}[/tex]

which is converges uniformly and absolutely for x > 0. I have shown that f is continous and has a derivative for x > 0. Now I have to show that [tex]f(x) \rightarrow 0[/tex] as [tex]x \rightarrow \infty.[/tex] It's obvious that it is the case, but how do I prove it. I've tried putting 1/x outside the sum, but then I don't know about the remaining part. Any ideas?

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