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

 

題目列表(包括答案和解析)

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

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設(shè)f(x)是定義在R上以6為周期的函數(shù),f(x)在(0,3)內(nèi)單調(diào)遞減,且y=f(x)的圖象關(guān)于直線x=3對(duì)稱,則下面正確的結(jié)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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設(shè)f(x)是定義在R上以6為周期的函數(shù),f (x)在(0,3)內(nèi)單調(diào)遞減,且y=f (x)的圖象關(guān)于直線x=3對(duì)稱,則下面正確的結(jié)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(shè)f(x)是定義在R上以6為周期的函數(shù),f(x)在(0,3)內(nèi)單調(diào)遞減,且y=f(x)的圖象關(guān)于直線x=3對(duì)稱,則下面正確的結(jié)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(shè)f(x)是定義在R上以6為周期的函數(shù),f(x)在(0,3)內(nèi)單調(diào)遞減,且y=f(x)的圖象關(guān)于直線x=3對(duì)稱,則下面正確的結(jié)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(xué)理數(shù)學(xué)理17,解:①         =2(1,0)                      (2分)             

        ?,                                        (4分)

?

        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(shè)雙曲線方程為:  ()                                 (1分)

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

,又為一條漸近線

, 解得:                                                     (5分)

                                                    (6分)

②設(shè),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(dāng)                                                      (8分)

(ii)當(dāng)

,  (),,

則有                                                                     (10分)

,

                                               (11分)

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

                                                 (13分)

20.解:①       

                                                        (2分)

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

  即                                (4分)

 

   即………………※              (6分)

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

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

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

當(dāng)

    (

                                          (11分)

                         (12分)

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

21.解:①設(shè)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(shè)   又

     

                                                         (4分)

同理可得 

                                                (5分)

又兩切點(diǎn)交于  ,

                               (6分)

③由  可得:

 

                                                (8分)

                  (9分)

 

當(dāng) 

當(dāng) 

                                                     (11分)

當(dāng)且僅當(dāng),取 “=”,此時(shí)

                                       (12分)

22.①證明:由,    

  即證

  ()                                    (1分)

當(dāng)  

      即:                          (3分)

  ()    

當(dāng)   

   

                                                         (6分)

②由      

數(shù)列

                                              (8分)

由①可知, 

                    (10分)

由錯(cuò)位相減法得:                                       (11分)

                                    (12分)