a0a2a1a2a3a2a4a2a5a2a6a2a4a8a7a8a9a8a10a8a3a8a4a8a11a8a12a8a5 2006 a13a2a14a2a15 a11a2a12a2a16a2a17a8a16a8a18a8a19a8a19a8a20 a21a23a22a23a24a26a25a28a27a30a29a23a31a23a32a23a33a35a34a36a31a23a24a23a37a23a38 310 a39 (3 a40a23a41a23a42a23a43a23a44a30a45 a32 150 a32 ) a46 a27a30a47a23a48a23a49a23a50a23a51a23a52a23a53a23a54a23a49a23a55a23a56a23a57 a44 a53a23a54a23a58a23a59a23a57a23a60a23a61a23a62a23a56a23a57a23a63a23a64a23a65a23a66a23a67 1 (15 a68 ) a69 a;b a70a72a71a72a73a72a74a72a75a72a76 x = 0 a77a72a78a72a79a72a80 y = 8 < : ax + b a81 x 0; x2 + 1 a81 x < 0: 2 (15 a68 ) a82a84a83 an > 0; a85a72a75 P1 n=1 1 an a86a72a87a72a88 a69a72a89a72a85a72a75 P1 n=1 1 an+1 a90 a86a72a87a72a91 3 (15 a68 ) a92 m;n 0 a93a72a94a72a75 a88 a69a72a95a72a68 R 1 0 x m(1 x)ndx a96a72a97 a91 4 (15 a68 ) a92 a > 0;f(x) a98 [ a;a] a99a72a96a72a100a72a101a72a96a72a102a72a74a72a75 a88a104a103Z a a f(x) 1 + ex dx = Z a 0 f(x)dx: 5 (15 a68 ) a92a105a74a105a75 f(x) a76a105a106a105a107 [a;b] a96a105a108a105a109a105a110a112a111a105a113a105a114a116a115a118a117a105a78a118a79a118a119 f0(a) = f0(b) = 0; a103a105a120 a76 2 (a;b) a70a72a121 jf00( )j 4(b a)2jf(b) f(a)j: 6 (15 a68 ) a92a72a122a72a97a72a74a72a75 f(x) a123a72a124a72a125a72a126a72a79a72a75a72a76a127a111a72a113 [a;b] a99a72a128a72a100a72a101 a88a104a129 a119 f(a) = 0; a103 max x2[a;b] jf(x)j pb a( Z b a jf0(t)j2dt)1=2; Z b a f2(x)dx 12(b a)2 Z b a jf0(x)j2dx: 7 (15 a68 ) a92 n a98a72a130a72a131a127a111a84a132 D a96a72a133a127a134a84a135a72a136a72a137 C a96a72a138a72a139a127a134 a88a104a103I C @u @nds = ZZ D (@ 2u @x2 + @2u @y2 )dxdy: 8 (15 a68 ) a92a127a140a84a137 : x2a2 + y2b2 = 1 a96a72a141a72a142a72a143a72a144a127a145a84a146a72a96a105a131a105a95a105a68a72a147a105a98 L a143 S, a148a72a149 J = H (b2x2 + 2xy + a2y2)ds; a103 J = S2L 2 a91 9 (15 a68 ) a150a72a151a72a95a72a68 R 1 0 dx 1+x3 a96a72a97 a88a104a152 a89a127a153a84a154 a90a72a155a72a156 a75a72a157a105a85a105a75 P1 n=1 ( 1)n 1 3n 2 a96a72a143 a91 10 (15 a68a159a158a160a69a127a140a84a137 x = acos3 t;y = asin3 t(a > 0) a161a72a162a72a137 y = x a163a72a164a72a144a72a146a72a96a127a140a84a131a72a96a72a165a72a131a105a95 a91 1