Hi all. I encountered the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

lim x->0 x * cot(x). My calculator gives the value of 1 for this limit, which can be corroborated by looking at the graph of y = x * cot(x).

However, I reason that it should be zero, because:

lim x->0 x * cot(x) = (lim x->0 x) * (lim x->0 cot(x))

= 0 * lim x->0 cot(x)

= 0 (because anything multiplied by zero is zero.)

Clearly, my reasoning is flawed. What is wrong with it? And what is the correct way to do this problem?

Thank you.

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# Simple limit question

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