1. 若函數(shù)的定義域?yàn)?img height="21" src="data:image/wmf;base64,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" width="53" />,則函數(shù)的定義域?yàn)椋?nbsp;  ).

A.                                                           B. 

C.                                                             D. 

2. 函數(shù)的凸區(qū)間是(   ).

A.                                                       B. 

C.                                                     D. 無,定義域都為凹區(qū)間

3.  (   ).

A.                                                                      B.   

C.                                                                D. 不存在

4. 設(shè)級數(shù)的收斂半徑為5,則級數(shù)的收斂區(qū)間為(   ).

A.         B.           

C. D. 

5. 微分方程的階數(shù)為(   ).

A. 3   B. 4

C. 6   D. 7

1.答案:D.解析:本題考查函數(shù)的定義域.

2.答案:B.解析:本題考查導(dǎo)數(shù)的應(yīng)用.

,令,即.

3.答案:B.解析:本題考查廣義積分.

原式.

4.答案:B.解析:本題考查冪級數(shù)的性質(zhì).

性質(zhì):逐項(xiàng)求導(dǎo)、逐項(xiàng)積分不改變冪級數(shù)的收斂半徑和收斂區(qū)間.

對冪級數(shù)逐項(xiàng)求導(dǎo):,根據(jù)上述結(jié)論,冪級數(shù)的收斂半徑也是5.令,則冪級數(shù)的收斂半徑為5,從而,即冪級數(shù)的收斂區(qū)間為,故選B.

5.答案:B.解析:本題考查微分方程的階.

因題中導(dǎo)數(shù)最高的階數(shù)是4,故微分方程是4階.注:為3階,為0階.

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