Добавил:

Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Национальный минерально-сырьевой университет «Горный»

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

attachments_22-12-2011_21-07-09 / semestr1_2

.pdf

Скачиваний:

Добавлен:

02.04.2015

Размер:

1.18 Mб

Скачать

☆

<<< < Предыдущая 1 2 3 4 5 6 7 8 910 / 1210 11 12 > Следующая >>>

/ 0

y = y( x) ,

y = y (t ),

x = x(t ) , /

yt8

xt8

d 2 y

27.

/ 0 y = y(x),

dx2

5x =

sin 2t .

= ln tgt

+ ,. xt8 yt8 :

cos 2t (2t )8

(sin 2t )8

= 2cos 2t

xt8 =

-(sin 2t )

1 .

(sin 2t ) 2

;

sin2 2t

ctgt

sin2 2t

y8 = [ln tgt]8

(tgt )8

tgt

cos2 t

sin t cos t

sin 2t

F /

yt8

xt8

sin2 2t

y8x =

2 cos 2t

= tg2t.

sin 2t

sin

2 2t

sin 2t cos 2t

F, y8x

= tg2t.

d 2 y

! dy "

d 2 y

% ,

dx2

& dx '

+ + / // 0 / 0, -

, / 0 dydx , :

		! dy "			8
d 2 y		$		%

	=	& dx 't
dx2			xt8

! dy " 8

$ % :

& dx 't

! dy " 8 $ % & dx 't

8	1		8	2
= ( tg2t )	=		(2t )	=		.
		cos2 2t			cos2 2t

206

d 2 y

2 cos 2t "

2sin2

tg2

= $

: $

dx2

cos2

sin2

cos2 2t , 2 cos 2t

cos 2t

2t '

4.2.D " ^ 1-2

" + - , "

" 0 0 / ' -/ " /-

>, -/ 17-0025, C -

" ^1 5,12,25,35,45; ^2 - 55,62,75,85,92.

*		1	2	3	4	5	6	7	8	9	0
,

-	1	1	2	3	4	5	6	7	8	9	10
-		41	42	43	44	45	46	47	48	49	50

"	2	51	52	53	54	55	56	57	58	59	60


*		1	2	3	4	5	6	7	8	9	0
,

-	1	11	12	13	14	15	16	17	18	19	20
"		61	62	63	64	65	66	67	68	69	70
	2
		91	92	93	94	95	96	97	98	99	100


*		L,J	<,	;,-	',	C,D	I,N	R,(	>	*	G,
											T
		@	O	Q	3	K	+	H		S
											U

-	1	21	22	23	24	25	26	27	28	29	30
"		31	32	33	34	35	36	37	38	39	40

	2	71	72	73	74	75	76	77	78	79	80
		81	82	83	84	85	86	87	88	89	90

207

		D " # F 1
; & 1-5 , "								> .
	x +	2z = 5,		3x 2 y	= 5,
1.	5	5y + 2z = 7 ,	2.	5	+ 3z = 2,
1.	3x	5y + 2z = 7 ,	2.	x + 2 y	+ 3z = 2,	x + y + 2z = 1,
	5	5y z = 2.		5		x + y + 2z = 1,
	4x +	5y z = 2.		2x + y + z = 2.		5	3y	z = 1,
					5.		3y	z = 1,
	x +	3z = 8,		4x + 5y	= 3,	5
	5	y + 4z = 10,		5	+ 2z = 5,	x + 3y + 2z = 1.
3. 2x +		y + 4z = 10,	4. 3x y		+ 2z = 5,
	5	6 y + z = 0.		5	+ 2z = 9.
	5x +	6 y + z = 0.		5x y	+ 2z = 9.

; & 6-10 , " /"# -

		x +	y + z = 3,
6.	5	x + 3y z = 1,

	5	2 y + z = 1.

	4x 2 y + 3z = 2,
8.	5	x	2z = 6,

	5	x	y + 2z = 2.

		y +	z = 4,
7.	5
7.	2x + 2 y 7z = 8,			x + 3y + 2z = 2,
	5	y	5z = 4.	x + 3y + 2z = 2,
	4x +	y	5z = 4.	5		z = 6,
	2x	3y	10.	3x 2 y +		z = 6,
	2x	3y	5z = 1,	5	2 y	z = 6.
9.	5	y +	2z = 0,		2 y	z = 6.
9.	2x +	y +	2z = 0,
	53x +	y	= 2.

D & 11-20 , "

11.

A(7;3;4), B(1;0;6),C(4;5; 2)

12.

A(2;0;0), B(0;3;0),C(0;0;6) D(2;3;8).

13.

a b

' 45o . > ', -

= 5 .

' a

3a + 2b ,

14.

' +

= 2i j + 3k

b = 3i j 2k ,

' , ' +-

15.

b = 3i 2 j .

H a = 2 j + 3k

= a × b ', ' a b .

16.

' ', ' -

b = i + j + k .

a = 2 j + k

208

17. > "b ,, ' OA,OB OC , ,

+ , "-

' + ' , 2.

r	r	= 2,	b	= 4, ' + -
r	r
18. H OA = a,OB = b ,	a

a b 60o . @ ' + OM - ' AOB OA .

19. > ' + a = 2m + 4n	r r
	b = m n , ' m, n - -

, " ' 120o .

20.H A(3;3; 2), B(0; 3;4),C(0, 3,0) D(0;2; 4). >

	r
	AB = a	CD = b 0 b a
	.
	D & 21-30 , " & 0 .
21.	>			,
	M1 (1; 1;2), M 2 (2;1;2) M 3 (1;1;4).
22.	D		Oz	,

2x + y 5z = 0 ' 60o . > , .

23.> + 4x + 3y 5z 8 = 0

4x + 3y 5z + 12 = 0.

24.> , (2; 1;1) -

3x + 2 y z + 4 = 0 x + y + z 3 = 0 .

	y = 3x 1,	2x + y + z 4 = 0.
25. > ' +		2x + y + z 4 = 0.
	2z = 3x + 2	x		y 1		z + 1
26.	>	x	=	y 1	=	z + 1
26.	>	2	=	1	=
	x + 2 y + 3z 29 = 0.	2		1	2
	x + 2 y + 3z 29 = 0.
27.	H x + y z = 0 , A(0;0;4)
	B(2;2;0). > ' +
	.

28.> 0 A(3;1; 1) x + 2 y + 3z 30 = 0 .

29.> , A( 1;2; 3) -

x = z,

y z = 1.

30. > , M1 (0; 5;0) M2 (0;0;2) x + 5y + 2z 10 = 0 .

209

;& 31-40 & & . G "

. ( " .

31.	y = (x + 2)2		18 y = (x 4)2
32.	x2 y 2 = 16		y = x + 1
33.	x2 + y2 = 1		y = x 1
34.	y2	= x	y = 2x + 1
35.	x2 + (y 2)2 = 7		3y2	= x2 3
36.	y2 x = 2		y 2	3x = 0
37.	(x 1)2 + y2 = 9		y2 = 4x
38.	(y 2)2	= x + 2	x + y = 2
39.	(x 2)2	y = 2	(x 1)2 + y = 3
40.	4x2 + y2 = 9		2x 3y + 3 = 0

;& 41-50 " & , 0 -

. G " , 0 & #/ 1 .

# 1 -

+ (z 1)

+ y2 + z2 16

+ y

41.

+ y

46.

+ y2

3 z

42.

+ y2 z 2 0

47.

+ y 2

5 z

+ y2 9

+ y 2

43.

+ y2 z 2

48.

+ y2

z 2 2

+ y2 z 2 0

+ y2

44.

+ y2 + z2 16

49.

+ y2

+ y2 z 2 8

+ y2

+ z 2 3

45.

+ y2 4z 2 6

50.

+ y2

+ z2 4

+ y2 z2 6

+ y2

z 2 0

210

D " # F 2

; & 51-60 , " 1 -

& & .

51.à)

52.à)

53.à)

54.à)

55.à)

56.à)

lim

sin

(3x4 )ln (1 4x2 )

1-cos (2x

)

tg2

(x 2)(

lim

sin3 ( x

lim

e3x 1

0 arctg2 (3x), ctg(6x)

lim

arctg

(

x2 6x

+ 9

)

( x 3)ln (x 2)

3 sin

1 , tg(3x2 )

lim (

)

1 6x3 1

lim

cos(6x2 ) 1

+o arcsin (

x5 )ln (1+ 3 x3 )

(

á)

lim

5 + x2

x2 + x

á)

lim

x2 2x

4x2 36

á)

lim

24 + x

x2 1

á)

lim

10 6x3 + 5x

4x2 2 + 3x3

16 + 2x3

á) lim . x 2 3x2 3x 18

á) lim	12x 3x2		.
	4x2 12x	16
x 4

57.à)

58.a)

59.a)

60.a)

lim

1)sin(4

)

0+o

3 1+ x 1

(1 cos

)ln(1+ 4x3 )

lim

0+o

arctg2 (4x2 )

(2x 1) , ctg

lim

0+o

arcsin

1) , arcsin (x +1)

lim

2 + x

1 cos (x +1)

á)

lim

5 + 9x4

á)

lim

10x5 2x2 +1

3x3 + 2x5

á)

lim

x 3

& x +

á)

lim

8 2x2

x 2

7 + x

; & 61-70 ) & , /- #; ) & "

& ; ) " & 0 -

& .

211

5 x 61. f (x) = 5 x .

1 x2 ï ðè x 0, 63. f (x) =

cos x ï ðè x > 0.

65. f (x) = ex 2 .

	f (x) = 2		x
62.			3+ x	.
64.	f (x) =	arcsin x ï ðè 1 x < 0,

		5x ï ðè x > 0.
	f (x) =		x
66.					.
		(x + 4)3

67.	f (x) =		x	ï ðè x		< 0,
		2e
		2 4x ï ðè				x > 0.
69.	f (x) =	x2			.
		64 x3

68.	7 4x ï ðè			x 1,
	f (x) =			x > 1.
	3ln x ï ðè
	f (x) = 5	x
70.		x +1	.

;& 71-80 # #

71.y = 1 x4 + x2 arcsin(x2 ) 21.

72.y = 2xarcctgx + ln(3x + 3) + 5.

73.y = ln (1+ x3 ) 2x3 , arc tgx3 7.

74.y = x3 arccos(x3 ) 1 x6 + 9.

75.y = x3 +1 2ln (x3 1) 8.

x3 1

76.y = x , arcsin2 x + 21 x2 arcsin x 2x 16.

77.y = cos2 (5x) + 5x ,sin (10x) + 6.

78.y = 1 4x 2x , arccos(2x ) 3.

79.	y =	1	arctg(2x) +	x	+ 20.
		2		1+ 4x2

80.	y = tg2 (3x) + 2ln			(cos(3x)) 11.

212

; & 81-85 & & "# Ox -

", 0 y = f (x)

( " .

y = e3x ,

y = x2 5x + 6,

81.

;e%.

82.

A(4; 2).

! x "

83.

y = ctg $

;1).

84.

y = arctgx,

A$1;

2 '

y = x3 + x,

4 '

85.

A(1; 2).

; & 86-90 & & "# Oy -

", 0 y = f (x) &.

( " .

		!		2	"
86.	y = cos ( x ),	!		2	"
86.	y = cos ( x ),	A$			;0%.
		&	4		'

		!				"
	y = arcsin x,	!		3		"
88.		A$			;		%.
88.		A$			;		%.
		$	2			3	%
		&	2			3	'

90. y = tg (5x),

; & 91-100 dy d 2 y dx dx2

87.	y = 16 x2 ,		A(3;7).
89.	y = ln(x3 ),		A(e;3).
!		"
A$		;1%.
A$	20	;1%.
&	20	'

, &-

213

		1
91.	5x(t) =		,
	5x(t) =	sin t	,
		sin t
	5
	y(t) = ctgt

x(t) = tg(2t),

y(t) = 4t.

95.x(t) = ln(1+ t2 ),y(t) = arctgt.

5x(t) = cos3 t, 97.

5 y(t) = 3ln (cos t ).

x(t) = arctg (t3 ),

99.5

5 y(t) = t3.

		2			t		,
92.	5x(t) =	2					,
92.							2t
	5 y(t) =								.
	5 y(t) =								.
			2t +1

					1 t ,
94.	5x(t) =				1 t ,
94.
	5 y(t) = arcsin										t	.


										1 t ,
96.	5x(t) = arccos									1 t ,
96.
	5 y(t) =					t		.

		1
98.	5x(t) =			,
	5x(t) =	t		,
		t
	5
	y(t) = arcctgt.

x(t) = sin(3t),

100.y(t) = ln (sin (3t )).

4.3. @ / "

@ &

			@ 1
					0 A =	0	1	2
						0	1	2
1. : ' " A			, a			3	2	1
		23	23			2	3	0
						2	3	0
	A) 2;	B) 1;	C) -3;		D) -2.
			5x + 4 y z = 2,
			5	+ 2z = 1,
2. O + x y				+ 2z = 1,
			5
			3x + 2 y + z = 3.
	A) - ,
	B) ,
	C) " + - ?
			2x y + mz = 5,
		5
3. m 2x + 3y + 2z = 1, ?
		5	2 y + 5z = 0
			2 y + 5z = 0		D) m = 0.
	A) m = 1;	B) m = 1;	C) m = 3;		D) m = 0.

214

x + y z = 0,
5	- ?
4. m x + 3y + z = 0,	- ?
5
x + 2 y + mz = 0

A) m = 1; B) m = 0; C) m = 2; D) m = 1.

		3x 3y z = 1,
5.	5
5.	x y + 2z = 2, ' x /
	5	x + y + 4z = 0
		x + y + 4z = 0

O.			D) x = 2.
A) x = 2;	B) x = 1;	C) x = 1;	D) x = 2.

x + 3y + z = 0
5
6. > - x + 7 y + 5z = 0 . @ .
5	x + y z = 0
	x + y z = 0
A) x = t, y = 2t, z = t;	B) x = 2t, y = t, z = t;
C) x = 2t, y = t, z = t;	D) x = t, y = t, z = 2t.

215

<<< < Предыдущая 1 2 3 4 5 6 7 8 910 / 1210 11 12 > Следующая >>>

Соседние файлы в папке attachments_22-12-2011_21-07-09

#
02.04.2015465.65 Кб10razdel 1.pdf
#
02.04.2015254.75 Кб10razdel 2.pdf
#
02.04.2015467.57 Кб10razdel 3.pdf
#
02.04.2015738.49 Кб11razdel 4.pdf
#
02.04.20151.03 Mб11semestr1_1.pdf
#
02.04.20151.18 Mб9semestr1_2.pdf
#
02.04.2015228.88 Кб16test11.pdf
#
02.04.201586.53 Кб26titul list.pdf

*		1	2	3	4	5	6	7	8	9	0
,

-	1	1	2	3	4	5	6	7	8	9	10
-		41	42	43	44	45	46	47	48	49	50

"	2	51	52	53	54	55	56	57	58	59	60


*		1	2	3	4	5	6	7	8	9	0
,

-	1	11	12	13	14	15	16	17	18	19	20
"		61	62	63	64	65	66	67	68	69	70
	2
		91	92	93	94	95	96	97	98	99	100


*		L,J	<,	;,-	',	C,D	I,N	R,(	>	*	G,
											T
		@	O	Q	3	K	+	H		S
											U

-	1	21	22	23	24	25	26	27	28	29	30
"		31	32	33	34	35	36	37	38	39	40

	2	71	72	73	74	75	76	77	78	79	80
		81	82	83	84	85	86	87	88	89	90

*		1	2	3	4	5	6	7	8	9	0
,

-	1	1	2	3	4	5	6	7	8	9	10
-		41	42	43	44	45	46	47	48	49	50

"	2	51	52	53	54	55	56	57	58	59	60


*		1	2	3	4	5	6	7	8	9	0
,

-	1	11	12	13	14	15	16	17	18	19	20
"		61	62	63	64	65	66	67	68	69	70
	2
		91	92	93	94	95	96	97	98	99	100


*		L,J	<,	;,-	',	C,D	I,N	R,(	>	*	G,
											T
		@	O	Q	3	K	+	H		S
											U

-	1	21	22	23	24	25	26	27	28	29	30
"		31	32	33	34	35	36	37	38	39	40

	2	71	72	73	74	75	76	77	78	79	80
		81	82	83	84	85	86	87	88	89	90

*		1	2	3	4	5	6	7	8	9	0
,

-	1	1	2	3	4	5	6	7	8	9	10
-		41	42	43	44	45	46	47	48	49	50

"	2	51	52	53	54	55	56	57	58	59	60


*		1	2	3	4	5	6	7	8	9	0
,

-	1	11	12	13	14	15	16	17	18	19	20
"		61	62	63	64	65	66	67	68	69	70
	2
		91	92	93	94	95	96	97	98	99	100


*		L,J	<,	;,-	',	C,D	I,N	R,(	>	*	G,
											T
		@	O	Q	3	K	+	H		S
											U

-	1	21	22	23	24	25	26	27	28	29	30
"		31	32	33	34	35	36	37	38	39	40

	2	71	72	73	74	75	76	77	78	79	80
		81	82	83	84	85	86	87	88	89	90