) ( 0)xxg x xx?????,而( ) 1 lnh x x x? ??在( 0, )??上单调递减,且(1) 0h?,当01x??,( ) 0hx?,即( ) 0gx??,()gx在( 0, 1)上单调递增,当1x?时,( ) 0hx?,即( ) 0gx??,()gx在(1, )??上单调递减,∴max( ) (1) 3g x g??.又0lim ( )xgx????,2242 ln 4 1li m ( ) li m li m 02x x xxxxgxxx??? ??? ??????? ??,如图,当132m??或102m??时,12ym??与()y g x?的图象只有一个交点,∴16m??或0m?.12分22.解:(1)由1 2 cosx???,3 2 siny???,得22( 1) ( 3 ) 4xy? ???……①将cossi nxy?????????代入①式,化简得2 3 sin 2 cos? ????.5分(2)直线l的直角坐标方程为20xy???,∴圆心( 1, 3 )C?到直线l的距离为312d??,∴弦长为222 2 2 3 6 2Rd? ????.10分23.解:(1)由已知得22()x a b??,则x a b???或x b a??,由题意得13abba? ???????,解得21ab??????,5分(2)由2 1 ( 2) ( 1) 3x x x x? ???????,得3 2 1 3xx? ?????∴m的取值范围??|3mm?.10分
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