2014/2015
f f(x) = 1+4x2
1 + x+1 + x2
f f
f f
f+
+
f−∞
−∞
f α α = 0.14
102f(α) = 0.48 102
f f
nNfn[0,+[f(x) = x5+n x 1
fnxnxn
nNfn+1 (xn) (xn)nN
(xn)nN`
xn
1
n(n xn)nN
xn(n xn)nN
xn1
n
2014/2015
(G, )H K (G, )
H K =zG
(x, y)H×K;z=x yK H =zG
(x, y)K×H;z=x y
zH K z1K H
H K (G, )H K K H
H K (G, )H K K H
(Z,+)
(Z,+)
nZnZ={xZ|kZ;x=nk}
nZnZ(Z,+)
(n, p)Z2nZ=pZn=±p
(Z,+) nZ
H(Z,+) A=HN
H{0Z}
H{0Z}
A
A b
bZH
aH r a b r H r = 0
H=bZ
(a, b)Z2
(d, p)N2|aZTbZ=pZaZ+bZ=dZ
d=ab p =ab
2014/2015
f f(x) = 1+4x2
1 + x+1 + x2
xR,1 + x2>0,1+4x2>0x6|x|=x2<1 + x21 + x+1 + x2>0
fR
f.
f.
fR
1 + x+1 + x2= 2 + x+1
2x21
8x4+(x4) = 2 ×1 + 1
2x+1
4x21
16 x4+(x4)
1
1 + x+1 + x2=1
2×11
2x+1
8x3+(x4)
f(x) = 1
2×11
2x+1
8x3+(x4)×(1 + 2x22x4+(x4))
f(x) = 1
21
4x+x27
16x3x4+(x4)
f Y =1
21
4X
t=1
xx+t
f(x) = f1
t=4 + t2
1 + t+1 + t24 + t2= 2 + 1
4t21
64t4+(t4)
f1
t=1
2×11
2t+(t2)×2 + 1
4t2+(t2)= 1 1
2t+1
8t2+(t2)
f(x) = 1 1
2x+1
8x2+1
x2
f Y = 1 +
t=1
xx−∞ t
f(x) = f1
t=4 + t2
1 + t1 + t24 + t2= 2 + 1
4t2+(t3) 1 + t1 + t2=t×
11
2t+1
8t3+(t3)
f1
t=1
t×2 + 1
4t2+(t2)×1 + 1
2t+1
4t2+(t2)=2
t13
4t+(t)
f(x) = 2x13
4x+1
x
f Y =2X1−∞
f α α = 0.14
102f(α) = 0.48 102
f f
2014/2015
x
f0(x)
f(x)
−∞ α+
0+
++
f(α)f(α)
11
1
2
nNfn[0,+[f(x) = x5+n x 1
fnR+
R+fn(0) = 1
lim
x+fn(x) = +
fnR+[1,+[!xnR+|fn(xn) = 0
fn(0) = 1< fn(xn)<1
n5=fn1
nfn0< xn<1
n
xn
nNfn+1 (xn) = xn>0fn+1 xn+1 < xn
(xn)nN
(xn)nN
(xn)nN`= 0
0< xn<1
n(n xn)nN
yn=n×xn1yn=yn
n5(yn)nN1yn
(n xn)nN
zn=yn1 = nxn11
n5(1 + zn)5+zn= 0 zn
zn1
n5xn=1
n1
n5+1
n5
2014/2015
H K (G, )H K =zG
(x, y)H×K;z=x y
zH K z =x y (x, y)H×K
z z1=y1x1z1K H
H K (G, )
zH K H K z1H K
z1K H z K H
zK H z =x y x K y H
z z1=y1x1H K H K
y1x1H K z H K
H K =K H
H K K H
+H K G eG
+zH K K H H K H K
+z z0H K G z =x y z0=x0y0x
x0H y y0K z z0=x(y x0)y0y x0K H =H K
x00 H y00 K y x0=x00 y00 z z0= (x x00) (y00 y0)
H K H K
H K G
H K (G, )H K K H
(Z,+)
(Z,+)
nZnZ={xZ|kZ;x=nk}
nZnZnZ
nZ(Z,+)
(n, p)Z2nZ=pZn p
n=±p
n=±p n p n Z=pZ
nZ=pZn=±pH(Z,+) A=HN
H{0Z}H= 0Z
H{0Z}
H
AA
ANb
bH H
kN, k b Hk b HbZH
aH r q a b r =abq
a H b q b ZH H rH
r < b b A r A =HNr
H r /Nr60r r >0
r= 0
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