2016华南理工大学考研真题625_数学分析.pdf
625uHnóÆ2016côÖa¬Æ ïÄ)ÆÁÁò£3Kþ§ÁòþçÁò7LKÓ£¤8¶¡µêÆ©Û·µÄ:êÆ, AêÆ, OêÆ, VÇØênÚO, $ÊÆØ31. (12©) ¦4limx!0+vuut1x +s1x +r1x vuut1x s1x +r1x:2. (12©)(½a;b, ¦¼êf(x) =8>>>>>:1x(1 cosax); x 03( 1;+1)S?, ¿¦§ê.3. (12©)O4limn!1 1n npn(n+ 1)(n+ 2) (2n 1):4. (12©)?ؼêy =8:(x2 +y2)sin 1px2 +y2; x2 +y26= 0;0; x2 +y2 = 03(0;0)?ëY ê3, ê3:(0;0)?ØëY, f(x;y)3:(0;0)?.9. (13©) (1) òarctanxÐm¤?ê, ¦Âñ».(2) |(1)y²= 4 43 + 45 + ( 1)n 42n+ 1 + :(3) |(2)¥úªCqO , I¦õÚ, Ø Ø¬L10 m(mg,ê).12 10. (13©) 3,4Ý/«DSPy =Qx:Áyu(x;y) =Z xx0P(x;y)dx+Z yy0Q(x0;y)dy+CPdx+Qdy¼ê, Ù¥C = u(x0;y0).11. (13©)Oe¡x2a2 +y2b2 +z2c22= x2a2 +y2b2¤¤NÈ.12. (13©)k´ê, Lx2 +xy+y2 = r2, _. ½ÂI(r) =ILxdy ydx(x2 +y2)k:¦ limr!+1I(r):13