20xx微積分?練習(xí)題和答案1精選(編輯修改稿)
2025-03-25 23:44 本頁面
【文章內(nèi)容簡介】 y1?xy]?(1?xy)[ln1(?xy)?yxy1?xy]。(4)?z?x1??x?2yxxy31y2?x?2yx(x?y)33?z,?y?xx?2yx2?。3x?y1?u(5)?x?yzxz?1,?u?y?1zyxzlnx,?u?z??yz2yxzlnx。(6)?u?x?z(x?y)z?12z1?(x?y),?u?y??z(x?y)z?12z1?(x?y),?u?z?(x?y)ln(x?y)1?(x?y)2zz。2.(1)zx?y,zy?x,zxx?0,zxy?1,zyy?。(2) zx?asin2(ax?by),zy?bsin2(ax?by),zxx?2acos2(ax?by),zxy?2abcos2(ax?by),zyy?2bcos2(ax?by).223 fx?y?2xz,fy?2xy?z,fz?2yz?x,fxx?2z,fxz?2x,fyz?2z,fxx(0,0,1)?2,fxz(1,0,2)?2,fyz(0,?1,0)?0.2224zx??2sin2(x?t2),zt?sin2(x?t2yt2),zxt?2cos2(x?t2)?0.t2),ztt??cos2(x?t2)2ztt?zxt??2cos2(x?)?2cos2(x?5.(1) zx??12yx2ye, zy?x1xex,dz??yx2yedx?x1xyexdy。(2) z?ln(x2?y),zx?2xx?y22,zy?yx?y22,dz?xx?y22dx?yx?y22dy。(3)zx2yx???2 , zy?2y2x?y1?()1?x?y1?ydx?xdyxx?2dz? ,。 222y2x?yx?y()xyz(4) ux?yzxyz?1,uy?zxyz?1yzlnx,uz?yxyzlnx, lnxdz.du?yzxdx?zxlnxdy?yxyz6. 設(shè)對角線為z,那么z?22x?y,zx?xx?y22,zy?yx?y22, dz?xdx?ydyx?y22當(dāng)x?6,y?8,?x?,?y??,?z?dz?6??8?(?)6?822=(m).7. 設(shè)兩腰分別為x、y,斜邊為z,那么z?zx?xx?y22x?y,22，zy?yx?y22, dz?xdx?ydyx?y22,設(shè)x、y、z的絕對誤差分別為?x、?y、?z,當(dāng)x?7,y?24,?x??x?,?y???z?dz?7?2422y?, z?7?2422?25z的相對誤差?zz??%.8. 設(shè)內(nèi)半徑為r，內(nèi)高為h，容積為V，那么V??rh,Vr?2?rh,Vh??r,dV?2?rhdr??rdh,222當(dāng)r?4,h?20,?r?,?h?,?V?dV?2??4?20???4??(cm).23
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