一、选择题(本大题共8个小题,每小题5分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的.)
-
-
2.
使不等式
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmath%3E)
成立的一个充分不必要条件是( )
-
3.
已知
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3Et%3C%2Fmtext%3E%3Cmtext%3Ea%3C%2Fmtext%3E%3Cmtext%3En%3C%2Fmtext%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
, 则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmn%3Ei%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3Cmn%3Ec%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmn%3Es%3C%2Fmn%3E%3Cmtext%3E%CE%B1%3C%2Fmtext%3E%3C%2Fmath%3E)
的值为( )
-
-
A . 3
B . -2
C . -2 或3
D . -3
-
6.
设在海拔x m处的大气压强是y Pa,y与x之间的函数关系为y=cekx , 其中c , k为常量.已知海平面处的大气压强为1.01×105 Pa,在1 000 m高空处的大气压强为0.90×105 Pa,则在600 m高空处的大气压强约为(参考数据:0.890.6≈0.93)( )
A . 9.4×104 Pa
B . 9.4×106 Pa
C . 9×103 Pa
D . 9×105 Pa
-
7.
已知
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
, 且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
恒成立,则实数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmath%3E)
的取值范围是 ( )
-
8.
已知函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmtext%3E++%EF%BC%8C+%3C%2Fmtext%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22left%22%3E%3Cmtd+columnalign%3D%22left%22%3E%3Cmn%3El%3C%2Fmn%3E%3Cmn%3Eo%3C%2Fmn%3E%3Cmsub%3E%3Cmrow%3E%3Cmn%3Eg%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmtext%3E++%EF%BC%8C+%3C%2Fmtext%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的值域为
R , 则实数
a的取值范围为( )
二、多项选择题(每小题6分,共3小题,共18分.在每个小题给出的四个选项中,有多项符合题目要求.全对的得6分,部分选对的得部分分,有选错的得0分.)
三、填空题(本大题共3小题,每小题5分,共15分,把答案直接填在答题卡中的横线上.)
-
12.
若复数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmtext%3Ei%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmtext%3Ei%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%E2%88%88%3C%2Fmo%3E%3Cmtext%3ER%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
是纯虚数,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3C%2Fmath%3E)
.
-
-
14.
已知边长为2的菱形
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
中,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3E%E2%88%98%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
是边
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
所在直线上的一点,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%E2%8B%85%3C%2Fmo%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
的取值范围为
.
四、解答题(本大题共5小题,共77分.解答应写出文字说明、证明过程或演算步骤.)
-
-
(1)
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EO%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmtext%3E%CE%BB%3C%2Fmtext%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmtext%3E%CE%BC%3C%2Fmtext%3E%3Cmover+accent%3D%22true%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmover%3E%3C%2Fmath%3E)
, 求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%CE%BB%3C%2Fmtext%3E%3Cmtext%3E++%EF%BC%8C+%3C%2Fmtext%3E%3Cmtext%3E%CE%BC%3C%2Fmtext%3E%3C%2Fmath%3E)
的值;
-
-
-
(1)
求函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的解析式;
-
(2)
当
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%88%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmtext%3E%CF%80%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmfrac%3E%3Cmrow%3E%3Cmtext%3E%CF%80%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%5D%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
时,求函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
的取值范围.
-
-
(1)
求角
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
的大小;
-
(2)
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmath%3E)
, 求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3E%E2%96%B3%3C%2Fmtext%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmath%3E)
的面积.
注:如果选择多个条件分别解答,按第一个解答计分.
-
18.
如图,正方体
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的棱长为1,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
分别为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的中点.
![](//tikupic.21cnjy.com/2024/07/02/b7/54/b754b4833513ff2c0535df599c8f784b.png)
-
(1)
证明:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3Cmn%3E%2F%3C%2Fmn%3E%3Cmn%3E%2F%3C%2Fmn%3E%3C%2Fmath%3E)
平面
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
.
-
(2)
求异面直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
所成角的大小.
-
(3)
求直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
与平面
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmi%3EE%3C%2Fmi%3E%3Cmi%3EF%3C%2Fmi%3E%3C%2Fmath%3E)
所成角的正切值.
-
19.
已知函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Ee%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Ee%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmath%3E)
是奇函数.(e是自然对数的底)
-
-
(2)
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
时,关于
x的不等式
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
恒成立,求实数
m的取值范围;
-
(3)
设
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ef%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 对任意实数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmo%3E%E2%88%88%3C%2Fmo%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmi%3En%3C%2Fmi%3E%3Cmn%3E%5D%3C%2Fmn%3E%3C%2Fmath%3E)
, 若以
a ,
b ,
c为长度的线段可以构成三角形时,均有以
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eg%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Ec%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
为长度的线段也能构成三角形,求实数
n的最大值.