问答题设函数f(z)当x≥0时连续可微，且f(0)=1．现已知曲线y=f(x)，x轴、y轴及过点(x，0)且垂直于x轴的直线所围成的平面图形的面积与曲线y=f(x)在[0，x]上的一段弧长的值相等，求函数f(x)．
问答题在xOy平面的第一象限求一曲线，使由其上任一点P处的切线，x轴与线段OP所同成的三角形的面积为常数k，且曲线通过点(1，1)．
问答题设f(x)连续且满足，求f(x)．
问答题设f(x)在(-∞，+∞)上满足对任意x，y恒有f(x+y)=e2yf(x)+f(y)cosx，又f(x)在x=0处可导，且f'(0)=1，求f(x)．
问答题求常数a，b，c，d的值，使得微分方程y"+ay'+by=(cx+d)e2x有一个解是y=ex+x2e2x．
问答题设f(x)在区间[0，+∞)上连续，且，求证：微分方程的一切解，当x→+∞时都趋于1．
问答题已知二阶常系数齐次线性微分方程的两个特解，写出相应的微分方程．
问答题Directions:Writeanessayof160—200wordsbasedonthefollowingphoto.Inyouressay,youshould1)describethephotobriefly,2)illustratethegoodofvolunteerworkwith(a)specificexample(s),and3)makeyoursuggestion(s)tofindvolunteerwork.YoushouldwriteitneatlyonANSWERSHEET2.
问答题一容器在开始时盛有液体100升，其中含净盐10公斤，然后以每分钟3升的速率注入清水，同时又以每分钟2升的速率将冲淡的液体放出．容器中装有搅拌器使容器巾的液体保持均匀，求过程开始后1小时溶液的含盐量．
问答题解下列微分方程．
问答题求微分方程y"+4y=3|sinx|在[-π，π]上满足的特解．
问答题设f(x)是连续函数，由所确定，求f(x)．
问答题设f(x)在[0，+∞)上连续，且f(0)＞0，设f(x)在[0，x]上的平均值等于f(0)与f(x)的几何平均数，求f(x)．
问答题求微分方程(y-x
3
)dx-2xdy=0的通解．
问答题设，其中f(x)为连续函数，求f(x)．
问答题对任意实数x＞0，设曲线y=f(x)上点(x，f(x))处的切线在y轴上的截距等于连续函数在区间[0，x2]上的平均值，求f(x)．
问答题若y(x)是[0，1]上的连续可微函数，且满足条件求y(x)的表达式．
问答题求微分方程3y'-ysecx=y4tanx的通解．
问答题求微分方程y′+ycosx=(lnx)e
-sinx
的通解．
问答题Practically speaking, the artistic maturing of the cinema was the single-handed achievement of David W. Griffith (1875-1948). (46)Before Griffith, photography in dramatic films consisted of little more than placing the actors before a stationary camera and showing them in full length as they would have appeared on stage. From the beginning of his career as a director, however, Griffith, because of his love of Victorian painting, employed composition. He conceived of the camera image as having a foreground and a rear ground, as well as the middle distance preferred by most directors. By 1910 he was using close-ups to reveal significant details of the scene or of the acting and extreme long shots to achieve a sense of spectacle and distance. His appreciation of the camera' s possibilities produced novel dramatic effects. (47) By splitting an event into fragments and recording each from the most suitable camera position, he could significantly vary the emphasis from camera shot to camera shot. Griffith also achieved dramatic effects by means of creative editing. By juxtaposing images and varying the speed and rhythm of their presentation, he could control tile dramatic intensity of the events as the story progressed. (48) Despite the reluctance of his producers, who feared that the public would not be able to follow a plot that was made up of such juxtaposed images, Griffith persisted, and experimented as well with other elements of cinematic syntax that have become standard ever since. These included the flashback, permitting broad psychological and emotional exploration as well as narrative that was not chronological, and the crosscut between two parallel actions to heighten suspense and excitement. In thus exploiting fully the possibilities of editing, Griffith transposed devices of the Victorian novel to film and gave film mastery of time as well as space. Besides developing the cinema's language, Griffith immensely broadened its range and treatment of subjects. (49) His early output was remarkably eclectic: it included not only the standard comedies, melodramas, westerns, and thrillers, but also such novelties as adaptations from Browning and Tennyson, and treatments of social issues. As his successes mounted, his ambitions grew, and with them the whole of American cinema. When he remade Enoch Arden in 1911, he insisted that a subject of such importance could not be treated in the then conventional length of one reel. Griffith' s introduction of the American-made multi-reel picture began an immense revolution. Two years later, Judith of Bethulia, an elaborate historic philosophical spectacle, reached the unprecedented length of four reels, or one hour' s running time. (50) From our contemporary viewpoint, the pretensions of this film may seem a little ridiculous, but at the time it provoked endless debate and discussion and gave a newintellectual respectability to the cinema.