Part a)I need help understanding a step in solving [tex]\lim_{x\rightarrow \infty}xsin(\frac{1}{x})[/tex](adsbygoogle = window.adsbygoogle || []).push({});

The textbook is suggesting I replace [tex]\frac{1}{x}[/tex] with y, so that I can get a limit in the form

[tex]\lim_{y\rightarrow 0}\frac{siny}{y}[/tex] which is understandably easy to solve. The part I don't understand is how the limit changes from x approaches inf to y approaches 0. I was running into the same confusion with this problem as well so perhaps I should post it.

Part b)Solve [tex]\lim_{x\rightarrow 0}\frac{sin4x}{sin3x}[/tex]

They then proceed in their next step to write it as [tex]\frac{\lim_{4x\rightarrow 0}4x(\frac{sin4x}{4x})}{\lim_{3x\rightarrow 0}3x(\frac{sin3x}{3x})}[/tex]

How do they get the 4x approaches 0 and 3x approaches 0, I understand it as a "this is the way to do it" and can do it easily, but I'd like to know what they are doing. Anyways, thanks

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# Homework Help: Limit of a sine function problem.

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