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19
2
y
x
=−ln sin2
2
π
π
5
9
5
≤≤x
40
Sx
xnx
n
=+ ++cos
cos
.....
cos2
2
3
yX= sin
01 1, ≤
≤
x
10
Sx
xx
n
n
n
=− ++−
+
+321
3
1
21!
.... ( )
()!
4
y
X
arctg
X
x
=
−
−+ln 1
2
01 08,,≤
≤
x
10
S
xx x
nn
n
n
=−++−
−
+
24
1
2
212
1
22 1
... ( )
()
5
ye
x
=
12≤
≤
x
15
S
xx x
n
n
=+ + + +1
12
2
!!
.....
!
6
ye
x
x
=⋅
cos
cos( sin )
π
π
4
4
01 1, ≤
≤
x
25
Sx
n
n
x
n
=+ + +1
4
1
4
cos
!
....
cos
!
π
π
7
y
x
= co
s
01 1, ≤
≤
x
10
S
xx
n
n
n
=− + +−1
2
1
2
22
!
.... ( )
()!
8
y
x
xx
=
−+
sin
cos
π
π
4
12
4
2
01 08,,≤
≤
x
40
Sx x x n
n
=+ ++sin sin .... sin
π
π
π
4
2
44
2
9
y
x
x
arctgX
=
+
−
+
+
1
4
1
1
1
2
ln
01 08,,≤
≤
x
3
Sx
xx
n
n
=+ + +
+
+541
541
.....
10
ye x
x
=
cos
cos(sin )
01 1, ≤
≤
x
20
S
xnx
n
=+ + +1
1
cos
!
....
cos
!
11
yxe
x
=+()12
2
2
01 1, ≤
≤
x
10
Sx
n
n
x
n
=+ + +
+
13
21
22
.....
!
12
y
xx
=− −
−+
1
2
1
2
3
2
ln(
cos )
π
01 08,,≤
≤
x
35
S
xx xn
n
n
=+ ++
cos cos
....
cos
π
π
π
3
1
2
3
2
3
2
13
yx=
1
2
ln
02 1, ≤
≤
x
10
S
x
x
x
xn
x
x
=
−
+
+
−
+
++
+
−
+
1
1
1
3
1
1
1
21
1
1
3
( ) ..... (
)
14
yx=−
1
43
2
2
()
π
π
π
5
≤≤x
20
Sx
xnx
n
n
=− + + +−cos
cos
.... ( )
cos2
2
1
22
15
y
x
arctgX
x
=
+
−
1
22
2
01 1, ≤
≤
x
30
S
xx x
n
n
n
=−++−
−
+
+
35
1
21
2
315
1
41
..... ( )
16
yx=−
ππ
2
84
π
π
5
≤≤x
40
Sx
xnx
n
=+ ++
−
−
cos
cos
...
cos( )
()
3
3
21
21
22
17
y
ee
xx
=
+
−
2
01 1, ≤
≤
x
10
S
xx
n
n
=+ + +1
22
22
!
....
()!
19
2 x π 9π 40 cos 2 x cos nx
≤x≤ S = cos x + +.....+
y = − ln 2 sin 5 5
2 2 n
3 y = sin X 0,1 ≤ x ≤ 1 10 x3 x 2 n +1
S = x− +....+ ( −1) n
3! (2n + 1)!
4 y = XarctgX − 0,1 ≤ x ≤ 0,8 10 x2 x4 x 2n
n +1
S= − +...+ ( −1)
− ln 1 + x 2 2 12 2n(2n − 1)
5 y = ex 1≤ x ≤ 2 15 x x2 xn
S = 1+ + +.....+
1! 2 ! n!
6
y=e
x cosπ 4
⋅ 0,1 ≤ x ≤ 1 25 π π
cos cos n
4 x +....+ 4 xn
cos( x sin π 4 ) S = 1+
1! n!
7 y = cos x 0,1 ≤ x ≤ 1 10 x 2
x 2n
S = 1− +....+ ( −1) n
2! (2n)!
8 x sin π 4 0,1 ≤ x ≤ 0,8 40 π π π
S = x sin + x 2 sin 2 +....+ x n sin n
y= 4 4 4
1 − 2 x cos π 4 + x 2
9 1 1+ x 0,1 ≤ x ≤ 0,8 3 x5 x 4 n +1
y = ln + S = x+ +.....+
4 1− x 5 4n + 1
1
+ arctgX
2
10 y = e cos x cos(sin x ) 0,1 ≤ x ≤ 1 20 cos x cos nx
S = 1+ +....+
1! n!
11 y = (1 + 2 x 2 )e x
2
0,1 ≤ x ≤ 1 10 2n + 1 2 n
S = 1 + 3x 2 +.....+ x
n!
12 1 0,1 ≤ x ≤ 0,8 35 π π π
y = − ln(1 − x cos x 2 cos 2 x n cos n
2 S= 3 + 3 +....+ 3
π 1 2 n
− 2 x cos + x2 )
3
13 1 0,2 ≤ x ≤ 1 10 x −1 1 x −1 3 1 x −1
y= ln x S= + ( ) +.....+ ( )
2 x +1 3 x +1 2n + 1 x + 1
14 1 2 π2 π 20 cos 2 x cos nx
≤ x≤π S = − cos x + +....+ ( −1) n
y = (x − ) 5
4 3 2 2
n2
15 1+ x 2
x 0,1 ≤ x ≤ 1 30 x3 x5 x 2 n +1
y= arctgX − S= − +.....+ ( −1) n +1 2
2 2 3 15 4n − 1
16 π2 π π 40 cos 3x cos(2n − 1) x
≤x≤π S = cos x + +...+
y= − x 5
8 4 3 2
(2n − 1) 2
17 e x + e−x 0,1 ≤ x ≤ 1 10 x2 x 2n
y= S = 1+ +....+
2 2! (2n)!
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