030611

1. 20061814558 556. 200719,7,15.4,4,,3.,,.

2. (1) . (2).

; . 3. ... .

1.(n) =0(k0) qn=0(|q|1). .

2... . 3. .

4.. (1) f(x); f(x)=0f(x) f(x)f(x)0.

(2)f(x)=0f(x)f(x)=0. (3). (4)y=f(x), .f(x).

1.1q(q0)nSn, Tn= , n=1,2,3 Tn. q=1Sn=n,Tn= , Tn=1.q1Sn= ,Tn= ,0q1 qn=0, Tn=1.

q1 Tn=

Tn= n.q1q1q Tn qn, |q|1 q0q.

2. (1) ( n)=b,a,b (2) = n, m,n. (1)= = a=3b= ,aba=3b= .

(2) = n.x2+mx+2x+2.x=2x2+mx+2=0m=3, n=1. .

3.2007a0f(x)=x1ln2 x2alnxx0. FxxfxFx0, x1xln2x2alnx1. f(x)=1 x0F(x)=xf(x)=x2lnx+2ax0F(x)=1 x0.

F(x)(02)(2+)x=2F(2)=22ln2+2a.

x(0,2)2(2,+)F(x)0+F(x)F(2)

a0F(x)F(2)=22ln2+2a0.x(0+)F(x)=x , f(x)0.x0f(x)0f(x)(0+).x1f(x)f(1)=0x1ln2x+2alnx0. x1xln2x2alnx+1. .

4.f(x)=ax3+bx23x, 1x. 1f(x) 211x1, x2|f(x1)f(x2)|kk 3A1mm2y=f(x)m.

](1) f(x)=3ax2+2bx3f(1)=f(1)=0 a=1,b=0. f(x)=x33x. 2f(x)=x33x, f(x)=3x23=3(x+1)(x1) 1x1f(x)0f(x)1,1f(x)max=f(1)=2, f(x)min=f(1)=211x1, x2|f(x1)f(x2)||f(x)maxf(x)min|2(2)=4. |f(x1)f(x2)|max=4.k4 k4 .

3f(x)=3x23=3(x+1)(x1)y=x33xA1m.Mx0, y0My0=x303x0 f(x0)=3(x201) k=3(x201)=kAM=2x303x20+m+3=0**AA1mx02x303x20+m+3=0.

g(x0 ) = 2x303x20+m+3g(x0 ) = 6x206x0g(x0)0x01x00, g(x0)00x01g(x0 ) = 2x303x20+m+3(0)(1+)(01)g(x0)x0=0, x0=1g(x)x02x303x20+m+3 = 0g(x)=g(0)=m+30,m3g(x)=g(1)=2+m0, m2a{m|m3m2} ..

5.2007f(x)= (mR, e=2.718 28. f(x) x0f(x)f 1(x), 0pq, f (qp)f1(qp)f1(q)f1(p). x0f(x)=ex1(0,+)f(x)=ex10 x0f(x)= x3+mx2 f(x)=x2+2mx=x(x+2m).

1m=0f(x)=x20, f(x)= x3(,0f(x)= x30. f(0)=0f(x)R. 2m0f(x)=x(x+2m)0 x0x2m. f(x)= x3+mx2(,0 f(x)R.

3m0, f(x)=x(x+2m)0 x0x2m.f(x)= x3+mx2(,2m2m0.f(x)x=2mf(2m)= m3+4m3= m30f(x)0+x=0f(0)=0. m0f(x) m30m0f(x).

x0y=fx=ex1 y+1=ex x=ln(y+1).f 1(x)=ln(x+1)(x0). 1f(qp)f1(qp).g(x)=f(x)f1(x)=exln(x+1)1(x0).g(x)=ex (0,+)g(x)g(0)=e0 =0.g(x)(0,+). g(x)g(0)=e0ln(0+1)1=0.0pqqp0 g(qp)=eqpln(qp+1)10.eqp1ln(qp+1), f(qp)f1(qp).

2f1(qp)f1(q)f1(p).ln(qp+1)ln(q+1)ln(p+1)=ln(qp+1)ln(q+1)+ln(p+1)=ln =ln =ln .0pq. 1, ln 0.ln(qp+1)ln(q+1)ln(p+1),f1(qp)f1(q)f1(p).

h(x)=ln(xp+1)ln(x+1)+ln(p+1), x(p,+). h(x)p,+)h(x)h(p).h(p)=0, h(x)0 x(p,+).q(p,+), h(q)0. :0pqf(qp)f1(qp)f1(q)f1(p). .

6.2007an, nN*, :a1=(10, 5), an=(xn, yn)=k(xn1yn1, xn1+yn1)(n2 ). k. 1|an| 2an1an(n2); 3k = a1a2,ana1b1b2, bn, , =b1+b2++bnO{Bn}B.(tn, sn) tn=t sn=sB(ts).)

1|an|= = = | k | | k | |an1|, (n2) |a1|=5 . |an|5 | k |. | an |= 5 ( | k |)n1

2anan1=k(xn1yn1, xn1+yn1)(xn1, yn1) =k(xn1 2 + yn1 2)= k |an1|2.

cosan, an1= = ,

k0an, an1= k0an, an1= .

(3) k = 2 4an, an1= ,3a1a1, a5, a9, a13,b1, b2, b3, b4,an a1= |a1| ,an= |an| = |a1|(| k |)n1bn=a4n3= |a1|(| k |)4n4=a1(4|k|4 )n1 =(10,5 ) ( )n1

=(tn, sn), tn = 101+( )+( )2++( )n1=10 tn=8 sn=5{Bn}B( 8,4 ).