38
39
15–17
MASALALAR YECHISH
49.
y=f
(
x
)
funksiya uchun
x
0
va
x
nuqtalarga mos
h
va Δ
y
ni hisoblang:
1)
f
(
x
)=4
x
2
–3
x
+2,
x
0
=1,
x
=1,01; 2)
f
(
x
)=(
x
+1)
3
,
x
0
=0,
x
=0,1.
50.
Agar
x
0
= 3 va Δ
x
= 0,03 bo‘lsa, berilgan funksiyalar uchun: a) funksiya
orttirmasini; b) funksiya orttirmasining argument orttirmasiga nisbatini
toping:
1)
f
(
x
)=7
x
– 5; 2)
f
(
x
)
=
2
x
2
–
3
x
; 3)
f
(
x
)
=x
3
+
2; 4)
f
(
x
)
=x
3
+
4
x.
51.
Agar
x
0
=
2 va Δ
x
=0,01 bo‘lsa, berilgan funksiyalar uchun: a)
funk siya
orttirmasini; b) funksiya orttirmasining argument orttirmasiga nisbatini
toping:
1)
f
(
x
)
=
– 4
x+
3;
2)
f
(
x
)
=
–8; 3)
f
(
x
)
=x
2
+
10
x
;
4)
f
(
x
)
=x
3
–10
.
52.
x
→
0 bo‘lsa, funksiya qaysi songa intiladi:
1)
f
(
x
)=
x
3
–2
x
2
+3
x
+4;
2)
f
(
x
)=
x
5
–6
x
4
+8
x
–7;
3)
f
(
x
)=(
x
2
–5
x
+1)(
x
3
–7
x
2
–11
x
+6);
4)
f
(
x
)=
2
2
19
7
28
x
x
x
x
− −
+
−
;
5)
f
(
x
)=
3
3
2
8
1
x
x
x
x
x
−
+
+ +
?
53.
Funksiyaning hosilasini toping:
1)
y=
17
x
;
2)
y=
29
x–
3;
3)
y=–
15;
4)
y=
16
x
2
–3
x
;
5)
y=–
5
x+
40;
6)
y=
18
x–x
2
;
7)
y=x
2
+
15
x
;
8)
y=
16
x
3
+
5
x
2
–
2
x+
14;
9)
y
=3
x
3
+2
x
2
+
x.
54.
Funksiyaning hosilasini: a)
x =
–3;
b)
x =
1,1; c)
x =
0,4; d)
x = –
0,2
nuqtalarda hisoblang:
1)
y
= 1 5
x
; 2)
y
=9
x
+3; 3)
y
=–20;
4 )
y
= 5
x
2
+
x
;
5)
y
=–8
x
+4; 6)
y
=8
x
–
x
2
; 7)
y
=
x
2
+25
x
; 8)
y
=
x
3
+5
x
2
–2
x
+4.
55.
y= f
(
x
) funksiya hosilasini ta‘rifga ko‘ra toping:
1)
( )
5
3
2
2
+
+
=
x
x
x
f
;
3*)
( )
x
x
x
f
1
+
=
;
2)
( ) (
)
3
2
+
=
x
x
f
;
4*)
2
1
( )
x
f x
x
+
=
.
40
41
56.
y
=
( )
x
f
funksiyaning
0
x
nuqtadagi hosilasini toping:
1)
f
(
x
)=4
x
3
+ 3
x
2
+2
x
+1,
x
0
=1
;
2)
( )
3
0
1
sin 22 ,
1
3
f x
x
x
=
+
°
= −
x
0
=–1
;
3)
( ) (
)
(
)
0
2 1
1 ,
4
f x
x
x
x
=
+
−
=
x
0
=4
; 4)
( )
3
0
2
1,
3
1
x
f x
x
x
−
=
= −
+
x
0
=–3
.
57.
Moddiy nuqta
5
3
4
)
(
3
+
−
=
t
t
t
s
qonuniyat bilan
harakatlanmoqda
(
s
metrda,
t
– sekundda). Moddiy nuqtaning 2-sekunddagi tezligini
toping.
58.
Funksiyaning hosilasini toping:
1)
x
x
y
2
1
+
=
;
2)
3
3
2
x
x
y
+
=
;
3*)
x
x
tg
x
x
y
3
5
log
−
⋅
+
=
tg
x
–log
3
x
;
4)
(
)
3
3
2
+
=
x
y
;
5*)
y = x
·ln
x
·(
x
+1);
6)
(
)(
)
2
−
+
=
x
x
x
y
;
7)
x
x
y
sin
2
+
=
; 8)
y
=10
x
+log
2
5+cos15°;
9)
x
y
x
sin
3
⋅
=
−
;
10*)
y
=tg
x
·cos
x
+7
x
·
x
7
;
11)
( )
3
8
4
1
2
4
+
−
=
x
x
x
f
; 12)
( )
5
sin
2
2
+
−
=
x
x
x
f
;
13)
10
( )
80
f x
x
x
=
−
; 14)
2
( ) 8
ln 2
x
f x
x
=
−
.
59.
Funksiya
hosilasining
x
0
nuqtadagi qiymatini hisoblang:
1)
( )
0
,
cos
1
0
=
=
x
x
x
f
x
0
= 0; 2)
f
(
x
)=(
x
2
+3
x
)ln
x
,
x
0
=1;
3)
2
arctg
( )
1
x
f x
x
=
+
,
x
0
= 1; 4)
f
(
x
)=e
x
(
x
–ln2),
x
0
=ln2.
60*.
0
)
('
>
x
f
tengsizlikni yeching:
1)
f
(
x
) =
x
·ln27–3
x
; 2)
( )
x
x
x
f
2
sin
−
=
;
61.
Moddiy nuqta
t
t
t
t
s
2
2
3
3
1
)
(
2
3
+
−
=
qonuniyat bilan harakatlanmoqda.
Moddiy nuqtaning tezligi qachon nolga teng bo‘ladi? Buning ma’nosi nima?