ВУЗ:
Составители:
Рубрика:
Амурский Государственный Университет 33
2.12
32
)3(49
xy −=
,
30
≤≤
x
.
−=
−=
).2sinsin2(
),2coscos2(
ttay
ttax
3
cos
3
ϕ
ρ
a=
.
2.13
22
2
−= xy
,
22
≤≤−
x
.
−=
+=
),cos(sin
),sin(cos
tttay
tttax
π
20
≤≤
t
2
θρ
=
,
πθ
≤≤
0
.
2.14
4
3
4
3
2
5
2
xxxxy −=
,
0
=
y
.
=
=
,sin2
,sin2
2
2
tgtay
tax
0
0
tt ≤≤
.
θρ
sin
a=
.
2.15
xy
cosln1
−=
,
6
0
π
≤≤
x
.
=
=
,sin
,cos
5
5
ty
tx
2
0
π
≤≤ t
.
3
cos
3
θ
ρ
a=
,
2
0
π
θ
≤≤
.
2.16
chxy =
,
10
≤≤
x
.
+=
−=
,2
,
3
1
2
3
ty
ttx
30
≤≤
t
.
ϕ
ρ
1
=
,
2
2
1
≤≤
ϕ
.
2.17
yx
cosln
=
,
3
0
π
≤≤
y
.
−=
+=
,cos8sin6
,cos6sin8
tty
ttx
2
0
π
≤≤ t
.
)sin1(4
ϕρ
−=
,
6
0
π
ϕ
≤≤
.
2.18
yyx
ln
2
1
4
1
2
−=
,21
≤≤ y
.
−=
−=
),cos1(9
),sin(9
ty
ttx
π
20
≤≤
t
.
)sin1(6
ϕρ
+=
,
0
2
≤≤−
ϕ
π
.
2.19
3
2
3
2
3
2
ayx =+
.
−=
=
,
,3
3
2
tty
tx
11
≤≤−
t
.
ϕ
ρ
3
4
2
e
=
,
22
π
ϕ
π
≤≤−
.
2.20
1
2
2
−=
x
y
,
0
=y
.
−=
=
,
4
2
,
6
4
6
t
y
t
x
.0
,0
=
=
y
x
ϕρ
2
=
,
12
5
0
≤≤
ϕ
.
2.21
)cos2ln(
xy
=
,
33
ππ
≤≤−
x
.
−=
=
),3(
3
,
2
2
t
t
y
tx
0
=y
.
ϕρ
sin
=
,
6
0
π
ϕ
≤≤
.
2.22
()
1ln1
2
1
22
−+−−=
xxxxy
,
11
+≤≤
ax
.
−=
+=
),sin(cos
),sin(cos
ttey
ttex
t
t
46
ππ
≤≤
t
ϕ
ρ
4
3
3
e
=
,
3
0
π
ϕ
≤≤
.
2.23
()
2
1
xx
ee
y
−
−−
=
,
30
≤≤
x
.
−=
−=
),2sinsin2(4
),2coscos2(4
tty
ttx
π
≤≤
t
0
.
),sin1(3
ϕρ
+=
0
6
≤≤−
ϕ
π
.
2.24
4arccos
2
+−−=
xxxy
,
2
1
0
≤≤ x
.
=
=
,sin6
,cos6
3
3
ty
tx
π
2
3
0
≤≤ t
.
),cos1(5
ϕρ
−=
0
3
≤≤−
ϕ
π
.
2.25
x
ey −=
2,
8ln3ln
≤≤ x
.
−=
−=
),cos1(3
),sin(3
ty
ttx
π
≤≤
t
0
.
ϕ
ρ
12
5
5
e
=
,
3
0
π
ϕ
≤≤
.
Амурский Государственный Университет 33
x =a (2 cos t −cos 2t ), ϕ
2.12 9 y 2 =4(3 −x) 3 , 0 ≤x ≤3 . ρ =a cos 3 .
y =a(2 sin t −sin 2t ). 3
x =a (cos t +t sin t ),
2.13 2 y =x 2 −2 , − 2 ≤x ≤ 2 . 0 ≤t ≤2π ρ =θ 2 , 0 ≤θ ≤π .
y =a (sin t −t cos t ),
2 2 x =2a sin 2 t ,
2.14 y = x 4 x − x 4 x 3 , y =0 . 2
0 ≤t ≤t 0 . ρ =a sin θ .
5 3 y =2a sin tgt ,
θ
ρ =a cos 3 ,
π x =cos 5 t , π 3
2.15 y =1−ln cos x , 0 ≤x ≤ . 5
0 ≤t ≤ .
6 y =sin t , 2 π
0 ≤θ ≤ .
2
1 3 1 1
x = t −t ,
2.16 y =chx , 0 ≤x ≤1 . 3 0 ≤t ≤3 . ρ = , ≤ϕ ≤2 .
2 ϕ 2
y =t +2,
ρ =4(1 −sin ϕ ) ,
π x =8 sin t +6 cos t , π
2.17 x =ln cos y , 0 ≤y ≤ . 0 ≤t ≤ . π
3 y =6 sin t −8 cos t , 2 0 ≤ϕ ≤ .
6
ρ =6(1 +sin ϕ ) ,
1 1 x =9(t −sin t ),
2.18 x = y 2 − ln y , 1 ≤y ≤2 . 0 ≤t ≤2π . π
4 2 y =9(1 −cos t ), − ≤ϕ ≤0 .
2
4
ϕ
2 2 2 x = 3t 2 , ρ =2e , 3
2.19 x +y =a .
3 3 3 −1 ≤t ≤1 .
3
y =t −t , π π
− ≤ϕ ≤ .
2 2
x =t 6 , x =0,
x2 6 5
2.20 y = −1 , y =0 . 4 ρ =2ϕ , 0 ≤ϕ ≤ .
2 y =2 − t , y =0. 12
4
x =t 2 ,
π π π
2.21 y =ln(2 cos x) , − ≤x ≤ . y = t (t 2 −3), y =0 . ρ =sin ϕ , 0 ≤ϕ ≤ .
3 3 6
3
2.22
1
2
(
y = x x2 −1 −ln x + x2 −1 , ) x =e t (cos t +sin t ), π
≤t ≤
π 3
ϕ
ρ =3e 4 , 0 ≤ϕ ≤ .
π
y =e (cos t −sin t ), 6 4
t
1 ≤x ≤a +1 . 3
x =4(2 cos t −cos 2t ), ρ =3(1 +sin ϕ ),
2.23 y=
(1 −e x
−e −x )
, 0 ≤x ≤3 .
y =4(2 sin t −sin 2t ), π
2 − ≤ϕ ≤0 .
0 ≤t ≤π . 6
y =arccos x − x −x 2 +4 , ρ =5(1 −cos ϕ ),
x =6 cos 3 t , 3
2.24 1 3
0 ≤t ≤ π . π
0 ≤x ≤ . y =6 sin t , 2 − ≤ϕ ≤0 .
2 3
y =2 −e x , x =3(t −sin t ), 5
ϕ π
2.25 0 ≤t ≤π . ρ =5e 12
, 0 ≤ϕ ≤ .
ln 3 ≤x ≤ln 8 . y =3(1 −cos t ), 3
Страницы
- « первая
- ‹ предыдущая
- …
- 31
- 32
- 33
- 34
- 35
- …
- следующая ›
- последняя »
