武汉大学考研试题 数学分析 2010.pdf

p,“2010 c 1 2 1 22 150156http:/ 2010 c)y 0,x1=a,xn+1=a+xn,n=1,2,3,.y:xn,limnxn.p,“2010 c 1 2 1 22 150156http:/ 1:K8 1(e)y.P l=1+1+4a2 1,Kdx2n+1=xn+a,l2=l+a,|xn+1 l|=|xn l|xn+1+l1l|xn l|1ln|x1 l|.l?limnxn=l=1+1+4a2.?3.(140)?f(x)3 0,2,f(2)=1/2Z0 xf(x)dx.y:(0,2),s.t.f()+f0()=0.y.dn,0,1/2,s.t.f(2)=12f()f()=2f(2).2d Rolle n,(,2)(0,2),s.t.0=()f()0()=f()+f0().?p,“2010 c 1 2 1 22 150156http:/ uyy(uxy)2=uxx uyy uxy uyx=vx 0(v)vy vy 0(v)vx=0.?5P.?5 (1)Monge-Amp ere.?5.(140)-x2+y2=az z=2a px2+y2(a 0)N?L.).LS=ZZx2+y2+ax2+y22a2q1+?2xa?2+?2ya?2+s1+?xx2+y2?2+?yx2+y2?2dxdy=ZZx2+y2+ax2+y22a2r1+4(x2+y2)a2+2#dxdy=2aZ0 r1+4r2a2+2!rdrp,“2010 c 1 2 1 22 150156http:/ 16+2!a2.?6.(140)y:?Xn=1ln(1+nx)nxn(a)3?m 1+a,),p a 0;(b)3(1,)SY.).dln(1+nx)nxnnxnxn=1xn11(1+a)n1,x 1+a(a 0)?3 1+a,)(a 0),l?3(1,)Y.?7.(140)?f(y)=Z0ex2cosxydx.(a)f(y)?.(b)y f(y)k?Y?.(c)f(y).).d?xmex2cosxy?xmex2(m N)9Z0 xmex2dx 0,?|f(x)f(y)|L|x y|,x,y (0,).y.(a)d?x y?p|x y|f(x)=x 3(0,)Y?.(b)d?1/(n+1)1/n1/(n+1)2 1/n2?=11/(n+1)+1/n n ,as n f(x)=x 3(0,)Lipschitz Y.?p,“2010 c12 122 150156http:/ 2:K8 85P.dd,?Lipschitz Y?Y?.?