问答题已知函数f(x，y)满足，且f(y，y)=(y+1)2-(2-y)lny，求曲线f(x，y)=0所围图形绕直线y=-1旋转所成旋转体的体积．

问答题求，其中D是由x2+y2=4和(x+1)2+y2=1所围成的平面区域．

问答题求幂级数的和函数f(x)及其极值．

问答题飞机以匀速v沿y轴正向飞行，当飞行到原点时被发现，随即从x轴上点(x 0 ，y 0 )处发射导弹向飞机击去，其中x 0 ＞0．若导弹的速度方向始终指向飞机，其速度大小为常数2v．

问答题计算

问答题设函数φ(x)在[0，1]上可导，并有其中a为实常数，试求φ(x)。

问答题设函数f(x)在|x|≤1上具有二阶连续导数，当x≠0时f(x)≠0，且当x→0时f(x)是比x高阶的无穷小．证明级数绝对收敛．

问答题{{B}}Directions:{{/B}} Read the following passage carefully and then translate each underlined part into Chinese.71. {{U}}It was not until modern scholarship uncovered the secret of reading Middle English that we could understand that Chaucer, far from being a rude versifier, was a perfectly accomplished technician, and that his verse is rich in music and elegant to the highest degree{{/U}}. 72. {{U}}Chaucer's own urbane personality is a delight to encounter in his books. He is avowedly a bookworm, yet few poets observe nature with more freshness and delight. He is a master of genial satire but can sympathize with true piety and goodness with as much pleasure as he attacks the hypocritical{{/U}}. 73. {{U}}It is not an uncommon estimate of Chaucer that he must be counted among the few greatest of English poets. In range of interest he is surpassed only by Shakespeare. He was recognized already in the Renaissance, when it came to England, as the Father of English Poetry. He was a man of wide learning and wrote with ease on religion, philosophy, ethics, science, rhetoric{{/U}}. No man has more completely summed up an age than Chaucer has his, yet the people of his great poems are revealed as men and women are in all times. Master of verse, as Chaucer was, he introduced into English poetry many verse forms; the heroic couplet (in which form most of The Canterbury Tales is written), verse written in iambic pentameter, rhyming aa, bb, cc, etc.——a form that was to be very important in the eighteenth century. The rime royal, a seven-line stanza in iambic pentameters, rhyming ababbcc (Troilus and Criseyde). The terza rima, three-line stanzas, rhyming aba, bcb, cdc, etc. (which he imitated from Dante, in some of his minor poems). And the eight line iambic pentameter stanza, rhyming ababbcbc( The Monk's Tale).

问答题设z=f(x+y，x-y，xy)，其中f具有2阶连续偏导数，求dz与．

问答题假设函数f(x)在[0，1]上连续，在(0，1)内二阶可导，过点A(0，f(0))与B(1，f(1))的直线与曲线y=f(x)相交于点C(c，f(c))，其中0＜c＜1． 证明：在(0，1)内至少存在一点ξ，使f"(ξ)=0．

问答题求

问答题求不定积分。

问答题设数列{an}满足a1=a2=1，且an+1=an+an-1，n=2，3，…．证明：在时幂级数收敛，并求其和函数与系数an．

问答题设函数f(x)可导，且f(0)=0，求f(x)．