Please help me to prove that the functions $f(x)=x$ and $g(x)=x−\frac{1}{x}$ satisfy the following property: $$ \forall\varepsilon>0\quad\exists\delta>0:\quad\forall x>0\quad(|f(x)-g(x)|<\delta\Rightarrow f(x)g(x)>\varepsilon) $$
A property of two functions
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calculus
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3What have you tried? Take any $\epsilon>0$. You have $|f(x)-g(x)|=1/|x|<\delta$, where you now want to pick a $\delta$ so that $f(x)g(x)>\epsilon$... – 2012-09-15