I Don't know how to start this question can someone please help me? Use the ordered field $\mathbb{R}$. For $|x−y|<0.01$ and $x,y\in(0,2),$ show that $|x^2−y^2|<0.04$
2026-03-25 16:46:24.1774457184
use the ordered field $\mathbb{R}$. For $|x−y|<0.01$ and $x,y\in(0,2),$ show that $|x^2−y^2|<0.04$ only use properties of absoulte values
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$$ |x^2-y^2|=|x-y| |x+y|<10^{-2}|x+y|\le10^{-2} (2+2)=0.04 $$