a)Ta thấy:
\(\left|x\right|+2003\ge2003\)
\(\Rightarrow\frac{1}{\left|x\right|+2003}\le\frac{1}{2003}\)
\(\Rightarrow\frac{2002}{\left|x\right|+2003}\le\frac{2002}{2003}\)\(\Rightarrow A\le\frac{2002}{2003}\)
Dấu = khi x=0
Vậy MaxA=\(\frac{2002}{2003}\Leftrightarrow x=0\)
b)Ta thấy:
\(-\left|x\right|\le0\)\(\Rightarrow-\left|x\right|+2002\le2002\)
\(\Rightarrow\frac{-\left|x\right|-2002}{2003}\le\frac{-2002}{2003}\Rightarrow B\le-\frac{2002}{2003}\)
Dấu = khi x=0
Vậy MaxB=\(-\frac{2002}{2003}\Leftrightarrow x=0\)