第1个回答 2010-06-28
4
.
1.
f(x) [a, b]
f(x) [a, b]
,
f(x)
[a, b]
f(x) [a, b]
.
2.
1
1+tan x
x = , .
3. x → 0, !"#$
(A) ax − 1(a> 0,a =1) (B) x − sin x
(C) 1 − cos 4x (D) ln(1 + √x)
% x&'()'*+ , , , .
4. lim n→∞
1
n
sin
π
n
+sin
2π
n
+ ··· +sin
(n − 1)π
n
=
1
0
dx = .
5., f(x)= x(x − 1)(2x − 1)(3x − 1) ··· (nx − 1),- f
(x) (0, 1). /0
.
1.234
1.5 lim x→0−(1 + x)
1
c|x|
= e2
,6 c7.
2., y = y(x)89Æ ey
+
y
0
et2
dt − x − 1=0:;<=,>? y = y(x)
@ABC
D6 y
|x=0.
3.6EF lim x→0
x2
0
(et2
− 1)dt
ln(1 + x6)
.4.6
ln x
√x
dx.
5.6
π
2
−π
2
(sin x +cos
4
x)dx.6.6
+∞
2
dx
x4
√
x2 − 1
.
G., f(x)=
x
1
e−t2
dt,6
1
0
f(x)dx.
H.,
f(x) [0, 1]
,I f(x) < 1,>?9Æ 2x−
x
0
f(t)dt =1 (0, 1)
.IJK/L.
M.68NOP y2 =2xQRP x = 1
2STUVWXRP y = −1YZ[U
\]].
^., f0(x) [0,+∞)
@ABC
,
f1(x)=
x
0 f0(t)dt
x
(1)_`ab;c f1(x) x =07,deab;cf
(gh f1(x))
[0,+∞)
.
(2)>? f1(x) <f0(x)(x> 0)I f1(x)i [0,+∞)
@ABC
.
(3)5 f2(x)=
x
0 f1(t)dt
x
, f3(x)=
x
0 f2(t)dt
x
, ··· , fn(x)=
x
0 fn−1(t)dt
x
,-jkl
x> 0,EF lim n→∞fn(x)m .
1