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问题 填空题

设y(x)在(-∞，+∞)连续，又当△x→0时α是比△x高阶的无穷小，函数y(x)在任意点处的增量△y=y(x+△x)-y(x)满足


且y(0)=π，则y(1)=______．

答案

参考答案：

解析： 先求y(x)，再求y(1)．为求y(x)先求y’(x)．将已知等式两边同除△x，并令△x→0，由连续性知

，于是取极限得


这是可分离变量的微分方程，分离变量得


[分析二] 将已知等式改写成


，由△y与微分dy的关系知，函数y(x)在任意点x处的微分为


其余解法同[分析一] ．


填空题

唐诗《枫桥夜泊》中有诗句“姑苏城外寒山寺，夜半钟声到客船”，在枫桥边客船里的人听到了寒山寺的钟声，是因为寒山寺的大钟受到僧人的撞击，产生 _________ 而发出的．客船上的人根据声音的 _________ 能辨别出传来的是“钟”声而不是“鼓”声或其他声音．

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单项选择题

For many people today, reading is no longer relaxation. To keep up their work they must read letters, reports, trade publications, interoffice communications, not to mention newspapers and magazines: a never ending flood of words. In (1) a job or advancing in one, the ability to read and comprehend (2) can mean the difference between success and failure. Yet the unfortunate fact is that most of us are (3) readers. Most of us develop poor reading (4) at an early age, and never get over them. The main deficiency (5) in the actual stuff of language itself—words. Taken individually, words have (6) meaning until they are strung together into phrases, sentences and paragraphs. (7) , however, the untrained reader does not read groups of words. He laboriously reads one word at a time, often regressing to (8) words or passages. Regression, the tendency to look back over (9) you have just read, is a common bad habit in reading. Another habit which (10) down the speed of reading is vocalization—sounding each word either orally or mentally as (11) reads.

To overcome these bad habits, some reading clinics use a device called an (12) , which moves a bar(or curtain) down the page at a predetermined speed. The bar is set at a slightly faster rate (13) the reader finds comfortable, in order to "stretch" him. The accelerator forces the reader to read fast, (14) word by word reading, regression and subvocalization practically impossible. At first (15) is sacrificed for speed. But when you learn to read ideas and concepts, you will not only read faster, (16) your comprehension will improve. Many people have found (17) reading skill drastically improved after some training. (18) Charlie Au, a business manager, for instance. His reading rate was a reasonably good 172words a minute (19) the training; now it is an excellent 1,378 words a minute. He is delighted that how he can (20) a lot more reading material in a short period of time.

第（6）空应选择（）

A．some

B．a lot

C．little

D．dull
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