Could you help me to show: $g(x,\epsilon)+f(x,\epsilon)=O(|\phi(x,\epsilon)|+|\psi(x,\epsilon)|)$ but $g(x,\epsilon)+f(x,\epsilon)\neq O(\phi(x,\epsilon)+\psi(x,\epsilon))$ (both when $\epsilon\to0$), where $O$ stands for the big Oh notation?
How to prove asymptotic property with big O notation?
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asymptotics
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0I suppose the assumption is that $g(x,\epsilon)=O(\phi(x,\epsilon))$ and likewise for $f$ with $\psi$? – 2011-02-21
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1Try $f(x)=g(x)=\phi(x)=x$ and $\psi(x)=-x$. – 2011-02-21