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        1. (Ⅱ)若方程有解.求的取值范圍. 得分評卷人 查看更多

           

          題目列表(包括答案和解析)

          一、選擇題(每小題5分,共50分)

            1.C  2.B  3.D  4.A  5.C  6.B  7.A  8.C  9.B  10.D

          二、填空題(每小題4分.共24分)

            11.5  12.4   13.3825   14.6ec8aac122bd4f6e 15.6ec8aac122bd4f6e   16.3

          三.解答題(本大題共6小題,共76分)

          17.(本題12分)

          解:(Ⅰ)∵6ec8aac122bd4f6e,

          6ec8aac122bd4f6e          ………………………(2分)

          6ec8aac122bd4f6e    ………………………(3分)

          6ec8aac122bd4f6e              ……………………(4分)

          ∵在6ec8aac122bd4f6e中,6ec8aac122bd4f6e

          6ec8aac122bd4f6e                             ………………………(5分)

          (Ⅱ)設(shè)6ec8aac122bd4f6e分別是6ec8aac122bd4f6e6ec8aac122bd4f6e的對邊,

          ∵?6ec8aac122bd4f6e

          6ec8aac122bd4f6e

          6ec8aac122bd4f6e    ①                                          ……………………(6分)

          由正弦定理:6ec8aac122bd4f6e,得 6ec8aac122bd4f6e             ……………………(7分)

          6ec8aac122bd4f6e

          6ec8aac122bd4f6e    ②                                          ……………………(8分)

          由①②解得6ec8aac122bd4f6e                                    ……………………(9分)

          由余弦定理,得6ec8aac122bd4f6e                       ………………(10分)

                           6ec8aac122bd4f6e

                           6ec8aac122bd4f6e                                       ………………(11分)

          6ec8aac122bd4f6e,即邊6ec8aac122bd4f6e的長為6ec8aac122bd4f6e。                              ……………………(12分)

           

          18.(本題12分]

          解:(Ⅰ)∵6ec8aac122bd4f6e是偶函數(shù),

          6ec8aac122bd4f6e,即6ec8aac122bd4f6e            ……(2分)

          6ec8aac122bd4f6e

          6ec8aac122bd4f6e                                  ………………………………(4分)

          6ec8aac122bd4f6e對一切6ec8aac122bd4f6e恒成立。

          6ec8aac122bd4f6e                                    ……………………………………(6分)

          (Ⅱ)由6ec8aac122bd4f6e                            ………………(7分)

          6ec8aac122bd4f6e

            6ec8aac122bd4f6e                                         …………………(8分)

            6ec8aac122bd4f6e

          錯誤!不能通過編輯域代碼創(chuàng)建對象。6ec8aac122bd4f6e                                           ……………………(10分)

          6ec8aac122bd4f6e6ec8aac122bd4f6e                                    …………………(11分)

          6ec8aac122bd4f6e6ec8aac122bd4f6e

          ∴若使方程6ec8aac122bd4f6e有解,則6ec8aac122bd4f6e的取值范圍是6ec8aac122bd4f6e6ec8aac122bd4f6e          ………………(12分)

           

          19.(本題12分)

          解:(Ⅰ) ∵6ec8aac122bd4f6e分別是6ec8aac122bd4f6e的中點,

          6ec8aac122bd4f6e6ec8aac122bd4f6e                                  ……………………(1分)

          6ec8aac122bd4f6e平面6ec8aac122bd4f6e,6ec8aac122bd4f6e平面6ec8aac122bd4f6e

          6ec8aac122bd4f6e平面6ec8aac122bd4f6e                                   …………………………(2分)

          6ec8aac122bd4f6e平面6ec8aac122bd4f6e6ec8aac122bd4f6e平面6ec8aac122bd4f6e,6ec8aac122bd4f6e平面6ec8aac122bd4f6e

          6ec8aac122bd4f6e                                          …………………………(4分)

          6ec8aac122bd4f6e6ec8aac122bd4f6e的中點,

          6ec8aac122bd4f6e6ec8aac122bd4f6e的中點.

          6ec8aac122bd4f6e                               ………………………(5分)

          6ec8aac122bd4f6e

          ∴四邊形6ec8aac122bd4f6e是平行四邊形                         …………………………(6 分)

          (Ⅱ)當(dāng)6ec8aac122bd4f6e時,平面6ec8aac122bd4f6e平面6ec8aac122bd4f6e                   …………………(8分)

          6ec8aac122bd4f6e上取一點,6ec8aac122bd4f6e連接6ec8aac122bd4f6e

          6ec8aac122bd4f6e當(dāng)6ec8aac122bd4f6e時,

          6ec8aac122bd4f6e,6ec8aac122bd4f6e

          6ec8aac122bd4f6e

                 6ec8aac122bd4f6e

                 6ec8aac122bd4f6e

          即當(dāng)6ec8aac122bd4f6e時,6ec8aac122bd4f6e,6ec8aac122bd4f6e                    ……………………(9分)

          6ec8aac122bd4f6e6ec8aac122bd4f6e,6ec8aac122bd4f6e

          6ec8aac122bd4f6e平面6ec8aac122bd4f6e                                       ……………………(10分)

          6ec8aac122bd4f6e

          6ec8aac122bd4f6e平面6ec8aac122bd4f6e                                 ……………………………(11分)

          6ec8aac122bd4f6e平面6ec8aac122bd4f6e

          ∴平面6ec8aac122bd4f6e6ec8aac122bd4f6e平面6ec8aac122bd4f6e                     …………………………………(12分)

           

           

           

          20.(本題12分)

          解:(Ⅰ) ∵6ec8aac122bd4f6e

          6ec8aac122bd4f6e                           ………………………………(2分)

          6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e上為減函數(shù)

          6ec8aac122bd4f6e≤O在區(qū)間6ec8aac122bd4f6e上恒成立                      …………………………(3分)

          6ec8aac122bd4f6e是開口向上的拋物線

          6ec8aac122bd4f6e6ec8aac122bd4f6e        6ec8aac122bd4f6e6ec8aac122bd4f6e      6ec8aac122bd4f6e6ec8aac122bd4f6e

          ∴只需              即                               …………………………(5分)

                  6ec8aac122bd4f6e6ec8aac122bd4f6e       6ec8aac122bd4f6e6ec8aac122bd4f6e

          6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e                             ………………………………………(6分)

          6ec8aac122bd4f6e6ec8aac122bd4f6e                                      

          6ec8aac122bd4f6e(Ⅱ)當(dāng)6ec8aac122bd4f6e時,                     

                                                

          ∴存在6ec8aac122bd4f6e,使得6ec8aac122bd4f6e

          6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e內(nèi)有且只有一個極小值點                      ……………(8分)

          6ec8aac122bd4f6e6ec8aac122bd4f6e                   

          6ec8aac122bd4f6e當(dāng)6ec8aac122bd4f6e時                      

           

          ∴存在6ec8aac122bd4f6e,使得6ec8aac122bd4f6e

          6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e內(nèi)有且只有一個極大值點                     ……………(10分)

          當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e時,由(Ⅰ)可知6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e上為減函數(shù)

          6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e內(nèi)沒有極值點.

          綜上可知,當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e時,6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e內(nèi)的極值點個數(shù)為6ec8aac122bd4f6e

          當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e時,6ec8aac122bd4f6e在區(qū)間6ec8aac122bd4f6e內(nèi)的極值點個數(shù)為6ec8aac122bd4f6e          ………(12分)

           

          6ec8aac122bd4f6e21.(本題14分)

          解:(Ⅰ)設(shè)橢圓的長半軸長為6ec8aac122bd4f6e,短半軸長6ec8aac122bd4f6e,半焦距為6ec8aac122bd4f6e,

          由離心率6ec8aac122bd4f6e,得6ec8aac122bd4f6e

          6ec8aac122bd4f6e

          6ec8aac122bd4f6e            ①                                     …………………(2分)

          ∵直線6ec8aac122bd4f6e的方程為6ec8aac122bd4f6e,原點6ec8aac122bd4f6e到直線6ec8aac122bd4f6e的距離為6ec8aac122bd4f6e

          6ec8aac122bd4f6e  ②                                     …………………(4分)

          ①代人②,解得6ec8aac122bd4f6e                            ………………………(6分)

          ∴橢圓的標(biāo)準(zhǔn)方程為6ec8aac122bd4f6e                        …………………………(7分)

          (Ⅱ) ∵6ec8aac122bd4f6e

          ∴?=6ec8aac122bd4f6e

          ∴?=?(-)=2                                    …………………(9分)

          設(shè)6ec8aac122bd4f6e,則6ec8aac122bd4f6e,即6ec8aac122bd4f6e                     ………………(10分)

          6ec8aac122bd4f6e

          ∴?=2

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