《第四届全国大学生数学竞赛预赛（数学类）试题评分标准.pdf》由会员分享，可在线阅读，更多相关《第四届全国大学生数学竞赛预赛（数学类）试题评分标准.pdf（4页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、?1:?15?z=3x2+4y2+1.?(x,y,z)?t?t(x,y,z)?5?tz=(3x2+4y2)t2+1,?t?10?=z2 4(3x2+4y2)=0.?15?22:?15?P?P?L?A(L).?A(L)?P?L?y=x2,P=(x0,y0)?1?P?y0 x20?2?L?y=k(x x0)+y0.L?x?x2=k(x x0)+y0,?x1 0,f(x)0 x 0,+).?R+01f(x)+f(x)dx +,?R+01f(x)dx +.?f(x)0,?0 ZN01f(x)dx ZN01f(x)+f(x)dx=ZN0f(x)f(x)(f(x)+f(x)dx1?1?limN+ZN0f(
2、x)f(x)(f(x)+f(x)dx limN+ZN0f(x)f(x)2dx=limN+(1f(x)|N01f(0)?8?Z+01f(x)dx Z+01f(x)+f(x)dx+1f(0)+?10?4:?10?A,B,C?n?P(t)=At2+Bt+C,f(t)=detP(t),?t?detP(t)?P(t)?f(t)?Re()0,b 0,c 0,?=b b2 4ac2a?6?b2 4ac 0?b2 4ac b,?Re=b b2 4ac2a 0;?8?b24ac 0?b2 4ac=i4ac b2,?Re=b/2a 0.25:?10?(1+x)n(1x)3=Pi=0aixi,|x|1,n?Pn1i
3、=0ai.?Pn1i=0ai?(1+x)n(1x)311x?xn1?2?(1+x)n(1 x)4=(2 (1 x)n(1 x)4=nXi=0(1)iCin2ni(1 x)i4,2?xn1?2n(1x)4n2n1(1x)3+n(n 1)22n2(1x)2n(n 1)(n 2)62n3(1x)1?xn1?6?2n3!(1 x)1)n2n12!(1 x)1)+n(n 1)22n2(1 x)1)n(n 1)(n 2)62n3(1 x)1?xn1?2n3!(n+2)(n+1)nn2n12!(n+1)n+n(n 1)22n2nn(n 1)(n 2)62n3.?n1Xi=0ai=n(n+2)(n+7)32n
4、4?10?26:?15?f:0,1 R?f(0)=f(1),R10f(x)dx=0,?f(x)6=1x 0,1.?n,?Pn1k=0f(kn)?12.?f(0)=f(1),?c (0,1)?f(c)=0?2?f(x)6=1,?f(x)1n(nXk=1g(kn)+1)=1nn1Xk=0g(kn)Z10g(x)dx=12?12?n1Xk=0f(kn)?=?n1Xk=0g(kn)+n 12?122?15?37:?25?A=?222a?,B=?4b31?.?(1)?AX=B?BY=A?a 6=2,b=4/3;(2)A?B?a=3,b=2/3;(3)A?B?a 2,b=3.?(1)?AX=B?B?A?B
5、Y=A?A?B?2?(A,B)?224b2a31?224b0a 211 b?B?A?a 6=2?6?(B,A)?(B,A)=?4b22312a?4b2201 3b/41/2a 3/2?.?A?B?b=4/3.?AX=B?BY=A?a 6=2,b=4/3?10?(2)?A,B?trA=trB,?|A|=|B|,?a=3,b=2/3?12?a=3,b=2/3,?A=?2223?,B=?42/331?,A?B?2 5+2.?2 5+2=0?A,B?A?B?15?(3)?A?A,B?B?b=3?16?B?g(x1,x2)=4x21+6x1x2+x22=(3x1+x2)2 5x21.?y1=3x1+x2,y2=x1?g(x1,x2)?y21 5y22?18?B?1?19?A?f(x1,x2)=2x21+4x1x2+ax22=2(x1+x2)2+(a 2)x22?z1=3x1+x2,z2=x2?f(x1,x2)?2z21+(a2)z22?22?A,B?A,B?a 2,b=3?25?24