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1 $begingroup$ I wanted to show that $f(x,y)=xsin y+ycos x$ sastisfy Lipschitz conditions. but I can't separate it to $L|y_1-y_2|$. According to my lecturer, the Lipschitz condition should be $$|f(x,y_1)-f(x,y_2)|le L|y2-y1|$$ I was able show that $x^2+y^2$ in the rectangle $|x|le a$, $|y|le b$ satisfies the Lipschitz condition, with my $L=2b$. But I had problem showing this for $f(x,y)=xsin y+ycos x $. real-analysis lipschitz-functions share | cite | improve this question edited Apr 5 '15 at 2:44 user147263