10.設是定義在R上的減函數(shù).且對于任意的.都有.若.則有 查看更多

 

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設f(x)是定義在R上的函數(shù),對任意實數(shù)m、n,都有f(m)·f(n)=f(m+n),且當x<0時,f(x)>1。
(1)證明:①f(0)=1;
②當x>0時,0<f(x)<1;
③f(x)是R上的減函數(shù);
(2)設a∈R,試解關于x的不等式。

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設f(x)是定義在R上以6為周期的函數(shù),f(x)在(0,3)內單調遞減,且y=f(x)的圖象關于直線x=3對稱,則下面正確的結論是


  1. A.
    f(1.5)<f(3.5)<f(6.5)
  2. B.
    f(3.5)<f(1.5)<f(6.5)
  3. C.
    f(6.5)<f(3.5)<f(1.5)
  4. D.
    f(3.5)<f(6.5)<f(1.5)

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f(x)是定義在R上以6為周期的函數(shù),f (x)在(0,3)內單調遞減,且y=f (x)的圖象關于直線x=3對稱,則下面正確的結論是

(A)f (1.5)< f (3.5)< f (6.5)         (B)f (3.5)< f (1.5)< f (6.5)     

(C)f (6.5)< f (3.5)< f (1.5)         (D)f (3.5)< f (6.5)< f (1.5)

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設f(x)是定義在R上以6為周期的函數(shù),f(x)在(0,3)內單調遞減,且y=f(x)的圖象關于直線x=3對稱,則下面正確的結論是

[  ]

A.f(1.5)<f(3.5)<f(6.5)

B.f(3.5)<f(1.5)<f(6.5)

C.f(6.5)<f(3.5)<f(1.5)

D.f(3.5)<f(6.5)<f(1.5)

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設f(x)是定義在R上以6為周期的函數(shù),f(x)在(0,3)內單調遞減,且y=f(x)的圖象關于直線x=3對稱,則下面正確的結論是

[  ]

A.f(1.5)<f(3.5)<f(6.5)

B.f(3.5)<f(1.5)<f(6.5)

C.f(6.5)<f(3.5)<f(1.5)

D.f(3.5)<f(6.5)<f(1.5)

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一.選擇題

1―5  CBABA   6―10  CADDA

二.填空題

11.       12.()       13.2          14.         15.

16.(1,4)

三.解答題

數(shù)學理數(shù)學理17,解:①         =2(1,0)                      (2分)             

        ?,                                        (4分)

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        ?

                cos              =

         

                由,  ,    即B=              (6分)

                                                       (7分)

                                                                (9分)

        ,                                                         (11分)

        的取值范圍是(,1                                                      (13分)

        18.解:①設雙曲線方程為:  ()                                 (1分)

        由橢圓,求得兩焦點,                                           (3分)

        ,又為一條漸近線

        , 解得:                                                     (5分)

                                                            (6分)

        ②設,則                                                      (7分)

              

        ?                             (9分)

        ,  ?              (10分)

                                                        (11分)

          ?

        ?                                        (13分)

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            單減區(qū)間為[]        (6分)

           

          ②(i)當                                                      (8分)

          (ii)當,

          ,  (),

          則有                                                                     (10分)

          ,

                                                         (11分)

            在(0,1]上單調遞減                     (12分)

                                                           (13分)

          20.解:①       

                                                                  (2分)

          從而數(shù)列{}是首項為1,公差為C的等差數(shù)列

            即                                (4分)

           

             即………………※              (6分)

          當n=1時,由※得:c<0                                                    (7分)

          當n=2時,由※得:                                                 (8分)

          當n=3時,由※得:                                                 (9分)

              (

                                                    (11分)

                                   (12分)

          綜上分析可知,滿足條件的實數(shù)c不存在.                                    (13分)

          21.解:①設過A作拋物線的切線斜率為K,則切線方程:

                                                                          (2分)

              即

                                                                                                             (3分)

          ②設   又

               

                                                                   (4分)

          同理可得 

                                                          (5分)

          又兩切點交于  ,

                                         (6分)

          ③由  可得:

           

                                                          (8分)

                            (9分)

           

           

           

                                                               (11分)

          當且僅當,取 “=”,此時

                                                 (12分)

          22.①證明:由,    

            即證

            ()                                    (1分)

            

                即:                          (3分)

            ()    

             

             

                                                                   (6分)

          ②由      

          數(shù)列

                                                        (8分)

          由①可知, 

                              (10分)

          由錯位相減法得:                                       (11分)

                                              (12分)

           

           


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