1、=2011cK)y 0; 0 0f 3x 0 f(1) =Z 10(u u2) sin2udu = 2 cos 1 sin 1:718p,2011 c1 2 1 58 718723 http:/ = 0;13 R3, p, 2ZZdxdydz(x2 +y2 +z2)p25.). 5B1 Bp3 Br = (x;y;z); x2 +y2 +z3 r2 25ZZB1dxdydz(x2 +y2 +z2)p2=Z 104 r2rp dr = 4 Z 101rp 2 dr.p 0;y 0).).1. =Z (3;2)(1;0)dpx2 +y2 =px2 +y2j(3;2)(1;0) =p14 1:(f)
2、 OZZzdxdy +xdydz +ydxdz, x2 + y2 = 1 z = 0 9z = 3 .p,2011 c1 2 1 58 718723 http:/ =ZZx2+y2 10 z 3zz +xx +( y)ydxdydzZZx2+y2 1z=3zdxdy= 3 3 = 0:2. K (3 60 = 180).(a) ef(x)3x = x0 NCk 3 0 ;L,?x2(x0 ;x0 + ) jf(x) f(x0)j Ljx x0j ;Kf(x) 3x0 :.). ! X f(x) = px3x0 = 0 ?K = 12, 3:.(b) ef(x;y) 3 (x0;y0) ,Sk
3、lim(x;y)!(x0;y0)f(x;y) 3, K limy!y0limx!x0f(x;y) 3.). ! X f(x;y) = ysin 1x 3 (0;0) ?, 43, g4 (kxy) 3.(c) f(x;y) 3 (x0;y0), Kf(x;y) 3 (x0;y0) :Y.). ! Xf(x;y) =(x2 sin 1x; x6= 00; x = 0.3. (150) x2 ; , y:sin x2jxj .p,2011 c1 2 1 58 718723 http:/ x2= sinjxj2 2 jxj2 = jxj :4. (150) y: sgn (x) =8:1; x 03
4、 1;1 Riemann , 3 1;1 3.y. sgn ( ) =kam:, Riemann ; , vk, .NN1am: ( 1).5. (150) f(x) R, F(x;y) = f(y x)2x F(1;y) = 12y2 y + 5.x0 0, xn+1 = F(xn;2xn) (n 0):y: limn!1xn 3.y. dK,F(1;y) = f(y 1)2 = 12y2 y + 5;f(y 1) = y2 2y + 10 = (y 1)2 + 9;f(x) = x2 + 9;9xn+1 = F(xn;2xn) = f(xn)2xn= x2n + 92xn : (1)l d
5、p,2011 c1 2 1 58 718723 http:/ xn+1 3 (, n 0);(b) xn+1xn= 12 + 92x2n1 (n 1)1 limn!1xn = a3. u (1) -n!1ka = a2 + 92a )a = 3:6. (150)f(x;y)3D R2 OzgCxyY, x, yN. y: f DY.y. 2.7. (120)ffn(x)g1n=130;1Y,3(0;1)S, ffn(x)g1n=130;1 k., ff0n(x)g1n=1 3 (0;1) k y: ffn(x)g1n=1kf.y. =L2 9 fnkg fng, 8“ 0; 9N 0; s:t
6、: nk;nk Nx20;1)jfnk(x) fnl(x)j “: (2)n5.(a) k3ffn(x)gY, =8“ 0; 9 0; jx x0j n2N)jfn(x) fn(x0)j “3:1Nk.n.2y(2)=-nl!1, y.3|jfn(x) fn(x0)j sup2(0;1)jf0n( )j jx x0j:p,2011 c12 158 718723 http:/ g49 fnkg fngffnk(xj)g1k=1 . p, xj = j 20;1 0;1 k. l ?“ 0,9N 0; s:t: nk;nl N8xj)jfnk(xj) fnl(xj)j “3:(c) (2):x20;1)9xj; s:t: jx xjj ;jfnk(x) fnl(x)j jfnk(x) fnk(xj)j+jfnk(xj) fnl(xj)j+jfnl(xj) fnl(x)j“:z1 y, = 2005 c), p, 1 2 120 , 138143.2 y, = 2007 c), p, 1 2 118 , 125131.4gA Weierstrass:n.