The rule say that:
Limit x->Anything 0*(sin x)=0.
Limit x->Anything 0*(cos x)=0.Does this apply here too?
Limit x->infinity (1/x)*(|cot x|)=0.I mean, Does the rule still apply here: Limit x->Anything 0*[0,infinity)=0 ?
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$\begingroup$No, it doesn't apply here, since $|\cot x|$ is not bounded. The correct rule is $$\lim_{x \to anything}(0)(\mbox{bounded})=0$$
Moreover, the limit $$\lim_{x \to \infty} \frac{|\cot x|}{x}$$ does not exist.
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