Литвин І.І., Конопчук О.М., Желізняк Г.О. Вища математика
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101
21. C( '9 9 ! & =
3
–3
2
–9+35
( – 4d d 4.
22. ( () 84 ' ( ,
7' 7 ' '9).
23. B 16 ( ( (( , 7' (
' 9).
24. 5! ! & = 3
5
–5
4
+4.
25. C ( :
1.
y = x
3
+ x
5
.
2.
y = 2x
4
+ x
1/3
.
3.
.
1
4
2
x
xy
4.
y = 3sinx + 2
x
+ 2e
x
.
5.
x
x
x
y ln
4
4
.
6.
y = 2sinx
.
7.
y = e
x
(1 + x
2
)
.
8.
.arcsintg2 xxy
C( ( '! ! ( !.
26.
,3
3
xxxy
x = 4.
27.
,tgsin xxy
4
S
x
.
28.
.1,
2
1
2
2
x
x
x
y
29.
.1,35ln
2
xxxy
x
30.
.4,
1
1
x
x
x
y
31.
.0,sin xxey
x
5. G. &" / 6&!*/
9.
.cos2 xy
x
10.
.
1
x
x
e
e
y
11.
.
1
2
2
x
x
y
12.
.
cos1
cos1
x
x
y
102
5. G. &" / 6&!*/
32.
.2,
432
432
x
xxx
y
33.
.2,3
32
xxxxxy
34.
,cosln)( xxf
3
S
x
.
35.
f(x) = sinx – cos
2
x
,
0
x
.
36.
f(x) = e
sinx
,
0
x
.
37.
,lnctg)(
x
x
f
4
S
x
.
38.
x
exf
2cos
,
4
S
x
.
39.
,4sinln)(
x
x
f
16
S
x
.
40.
f(x) = cos
2
x
2
,
2
S
x
.
41.
f(x) = e
sin2x
– 3cos2x
,
0
x
.
42.
f(x) = tg
2
3x
,
0
x
.
43.
,
1
)(
2
z
z
zf
3 z
.
44.
,3)(
34
x
exf
0
x
.
45.
,
1
1
ln)(
2
x
x
xf
2
x
.
46.
,
1
)(
2
x
x
xf
5 x
.
103
47.
,
1
9
)(
2
x
x
xf
22 x
.
48.
1
1
ln)(
x
x
xf
,
2
x
.
49.
,
3
)(
33 xx
ee
xf
0
x
.
50.
1
4
ln)(
2
2
x
x
xf
,
2
x
.
51.
13)(
2
x
exf
,
0
x
.
52.
,
1
)(
2
x
x
xf
4
x
.
53.
3
2
2
4
4
ln)(
x
x
xf
,
2
x
.
54.
xx
xx
ee
ee
xf
)(
,
1
x
.
55.
),()(
3
xxxxf
1
x
.
56.
x
x
xf
ln1
ln
)(
,
e
x
.
57.
1ln)(
22
xxf
,
1
x
.
58.
xxxf 1cos)(
,
1
x
.
C( ( ( '! ! ( !.
59.
2
42
x
x
y
,
1
x
.
5. G. &" / 6&!*/
104
5. G. &" / 6&!*/
60.
43
65
x
x
y
,
2
x
.
61.
2
6
3
x
xy
,
1
x
.
62.
,
2
76
2
34
x
xx
y
2
x
.
63.
,8
4
3
4
1
xxy
1
x
.
64.
,94
2
5
2
7
xxy
9
x
.
65.
,
3
6
x
xy
1
x
.
66.
,36
3
xxxxy
1
x
.
67.
,26
7
2
3
2
xxxy
1
x
.
68.
2
3
22
4
7
92
x
xxxy
1
x
.
69.
),47)(23(
x
x
y
2
x
.
70.
),443)(52(
2
xxxy
2
1
x
.
71.
),5)(54(
23
xxxy
1
x
.
72.
),92)(29(
23
xxxy
4
3
x
.
73.
)1)(3
2
( xx
x
y
,
1
x
.
74.
32
2
11
3
x
x
xy
,
1
x
.
105
5. G. &" / 6&!*/
75.
,
25
1
x
x
y
2
x
.
76.
,
73
32
x
x
y
1
x
.
77.
,
3
5
x
x
y
1
x
.
78.
,
1
1
x
x
y
4
x
.
79.
,
1
x
x
y
9
x
.
80.
2
3
2
1
3
x
xxy
,
9
x
.
81.
,
1
x
x
y
2
x
.
82.
,
3
5
2
x
x
y
1
x
.
83.
,
47
1
x
x
y
1
x
.
C( '9 9 ! ( :
84.
,136
2
xxy
]6;0[
x
W
.
85.
32
3
1
2
1
xxy
,
]3;1[
x
W
.
86
,6
32
xxy
]6;1[
x
W
.
87.
,3593
23
xxxy
]4;4[
x
W
.
88.
,10249
23
xxxy
]3;0[
x
W
.
89.
,32
23
xxy
]4;1[xW
.
90.
,1862
23
xxxy
]4;0[
x
W
.
91.
518
24
xxy
,
]2;2[
x
W
.
106
5. G. &" / 6&!*/
( ) () ( '( :
92.
xxy
3
3
1
.
93.
96
23
xxy
.
94.
45
24
xxy
.
95.
23
32 xxy
.
96.
23
23
xxy
.
97.
.3
3
xxy
98.
233
23
xxxy
.
99.
xxxy
23
2
.
100.
1
2
1
3
1
23
xxy
.
101.
44
4
xxy
.
102.
85
23
xxy
.
103.
xxxy 6
2
5
3
1
23
.
104. A! <
tS
2
sin
. C(
! t, ! ()< 1.
105. C( 9( !, <
tS 2sin
! ( S – , t – ().
106. A! <
32
3
1
23
ttS
(). C(
9( ! ! t = 3 .
107. A! <
.452
3
1
23
ttS
"'!
9( ! t = 5 c.
108. ! )
14
3
2
23
1
tttS
107
5. G. &" / 6&!*/
811
2
1
3
2
23
2
tttS
. 5 ! 9( '( ?
109. A! <
tS
2
sin
. C !,,
).
110. A ? )< ! t ? = 0,2t
2
. R 9(
! t = 10 c.
111. H # )< ( ! t #=0,4t
2
(S –
, t – (). C 9(
(.
112. A! <
42
23
ttS
. C
!, 1.
113. A! <
42
23
ttS
. C -
! ! t = 3c.
114. A! <
tttS 542
23
. C 9(-
! ! t = 2 c.
115. ! )
tttS 542
23
1
23
2
5,12 ttS
. C-
!, 9( .
116. A! < 9() )<
1126
2
ttV
. C !, ! 2.
117. H # )< ( ! t #=0,4t
2
(t –
(, # – ). C 9( !
t = 8c.
118. C 9( ! ! t=3c, 7
<
45
23
ttS
.
119. A < S = S(t). W , 7
S
c
(t) = 1?
120. A < S = S(t). W , 7
S
cc
(t) < 0?
121. A <
cbtattS
2
)(
. / -
! , b, '( ?
122. A <
cbtattS
2
)(
. / -
! , b, '( ?
123. C !
)sin()(
M
wtAtS .
108
5. G. &" / 6&!*/
124. A <
2
)(
2
0
at
tatS
(
0
, – ).
/ (9
0
, ?
125. A <
323)(
2
tttS
. 5
! ?
126. A! <
43
24
)(
2
34
t
tt
tS
. 5
! )?
127. C (! ( '
12
2
xy
!
'
.1,0,1
321
xxx
128. C < (!, ( ( '
2
xy
:
a) ! (;
') ! (3; 9);
) ! (–2; 4);
) ! )
.23 xy
129. 5 ! < (! ( '! '
3
xy
()< 3?
130. 5 ! (! ( '! ' :
a) ;
') )< ) ?
131. /( ) ' ?
132. 5 ! (! ( ' :
a)
') ( (
) )< ) ?
133. / ) ( !,
:
152)(
24
ttttS
,
2
12)( ttS
(( ! ! ) ( .
134. C , )!
:
1.
sin
lim
sin
x
x
x
x
x
of
.
2.
32
3
2
44
lim
12 16
x
x
xx
x
x
o
.
3.
lim
ln(1 )
x
x
x
of
.
4.
2
5
lim
3
x
tg x
tg x
S
o
.
109
5.
0
ln sin
lim
ln sin 5
x
x
x
o
.
6.
2
cos 3
lim
cos
x
x
x
S
o
.
7.
0
2
lim
1cos2
xx
x
ee
x
o
.
8.
2
1
lim
x
x
x
of
.
9.
0
arctg2
lim
arcsin 5
x
x
x
o
.
10.
3
0
lim ln
x
x
x
o
.
11.
2
1
lim( )
cos
tg
S
M
M
M
o
.
12.
1
1
lim
ln 1
x
x
xx
o
§·
¨¸
©¹
.
13.
0
11
lim
sin
t
tt
o
§·
¨¸
©¹
.
14.
2
lim cos tg 5
x
x
x
S
o
.
5. G. &" / 6&!*/
15.
2
0
lim
x
x
x
e
o
.
16.
57
1
57
lim
11
x
xx
o
§·
¨¸
©¹
.
17.
0
1
lim ctg
M
M
M
o
§·
¨¸
©¹
.
18.
0
1
lim
3
sin
3
x
x
ctg
x
o
§·
¨¸
¨¸
¨¸
¨¸
©¹
.
19.
0
lim ctg ln
x
x
x
xe
o
.
20.
1
2
lim sin(2 1) tg
x
x
x
S
o
.
21.
1
lim 1
x
x
x
e
of
.
22.
lim cos
x
x
m
x
of
§·
¨¸
©¹
.
23.
ln 2( 1)
10
lim 1
a
x
x
x
o
.
24.
1
ln
0
lim 2
x
x
x
o
.
110
:%!
#+ &:%!:.
/!+%F!!
'%;!< ;%: &c– 9(
( !
.
&cc – ;
S – 9; Sc=V – 9(
-!< ;%:
(! (
( !.
&c(
0
)=tgD
*!! &:%!, %$!! /*!+%,.
: %$!! /*!+%,.
1. C D(&).
2. C ! ! (
) &
c
; ) ’
&c=0, ' &c– <.
3. 5
! .
4. C !
!.
5. C ( !.
6. /'( .
yc>0f(x)n
y
c
<0f(x)p
yc=0 !
yc- !
<
&c- <
'x=x
2
–x
1
–
'&=&
2
–&
1
=&(
2
)–(
1
)=
=&(
1
+')–&(
1
) –