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hpfan101
 one year ago
\[\lim_{x \rightarrow 0^}(\frac{ 1 }{ x }\frac{ 1 }{ \left x \right })\]
hpfan101
 one year ago
\[\lim_{x \rightarrow 0^}(\frac{ 1 }{ x }\frac{ 1 }{ \left x \right })\]

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When \(x\to0^\), that means that \(x<0\), so \(x=x\). \[\frac{1}{x}\frac{1}{x}=\frac{1}{x}+\frac{1}{x}=\frac{2}{x}\]

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok, thank you! So if there's an absolute value and x is less than 0, we just change the sign?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Kind of, it depends on the values of \(x\) you're considering. The absolute value of a number is defined by \[x=\begin{cases}x&\text{for }x\ge0\\x&\text{for }x<0\end{cases}\] This means whenever \(x\) is some positive number, its absolute value is the same number, i.e. \(x=x\). If \(x\) is a negative number, then the absolute value will cancel that sign to make it positive. But it wouldn't be true that \(x=x\) because \(x\) is negative. For example, the previous equation would suggest that \(2=2\), but that's not true. We make up for the sign by making \(x=x\) whenever \(x\) negative.

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Oh I see. Thanks for the explanation!
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