I was wondering why when solving this limit, you are not allowed to do this:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]{ lim }_{ x\rightarrow 0 }\quad xsin(\frac { 1 }{ x } )[/itex]

Break this limit into:

[itex] { lim }_{ x\rightarrow 0 }\quad x\quad *\quad { lim }_{ x\rightarrow 0 }\quad sin(\frac { 1 }{ x } ) [/itex]

Then, since, sin(1/x) is bounded between -1 and 1, and lim x-> 0 (x) is 0, the answer should be 0.

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# Lim x to 0 x*sin(1/x)

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