MV3047

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Одесский национальный политехнический университет

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[НЕСОРТИРОВАННОЕ]

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d ) y = (x2 + 4)

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<<< < Предыдущая 1 2 3 45 / 65 6 > Следующая >>>

										41
										=9
	2	2	3		5		1	1 2			2	3	3	x	1		7	1	2
	2	2	3		5		1	1 2			2	3	3	x		2	18 1		1
	1	1	2				2	1	0		2	1	1	1		2	18 1		1
A =	1	1	2	B =	1	C =	2	1	0	D =	2	1	1	X = x2	F =	3	25 2		1
	4	1	4				3	0	5		6	2	1			3	25 2		1
	4	1	4		2		3	0	5		6	2	1	x3		0	4	1	5
																0	4	1	5

1.< #8 G = AC 2(D + A) ;

2.$!’%$# /# & & ! % % AY = D ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

lim

1 5x6

, b) lim

2x +1

x + 6

c) lim

+ 2x 8

2x2

7x 15

x3 8

x x6 + 3x3 +1

x 5

x 2

d )

, e)

x 6

5 x+2

lim

tg(5x)

x 0

x x + 4

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! ,, '#" & #

x ,

x 1;

. -( (!# *+ " +( "2 ,: F (x) =

x2 ,

x > 1

< #8 y/ 5% #6 (. ' +( "2 8:

a) y = 3(3

+ 2

); b) y = arcsin(2x) ln(

)

sin(x)

y =

1 cos(x)

d ) y = (x2 1)sin x

x2 + 5

2x + 1

<#. 6# & ! % % , # &/#5

*+ "# +( "2 , y =

! 2

$ #-62 -

6 @ x = 1 .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

	)x					1	tg ( x)
	ln(1 x) + tg	2
a) lim			;	b) lim
	ctg()x)
x 1				x 0	x

										42
								=10
2 1			1		1		1	4	1	1 2 1			x		4	8	12	0
2 1			1		1		1	4	1	1 2 1			x		3	9	12	3
	3	4 2					2	6	2		1	4 1	1		3	9	12	3
A =	3	4 2		B =	1	C =	2	6	2	D =	1	4 1	X = x2	F =	2	2	0	6
	0	1	1				3	8	2		2	6 2			2	2	0	6
	0	1	1		0		3	8	2		2	6 2	x3		1	3	4	1
															1	3	4	1

1.< #8 G = CD (D + 2A) ;

2.$!’%$# /# & & ! % %YC = D ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

14x5 + 3x

3x +17

2x +12

a) lim

, b) lim

, c) lim

2x5 + 7x +1

x2 + 8x +15

1 x

1 x2

x 5

x 1

d ) lim	xtg(3x)	x 1	x2
		, e) lim
	cos(x) cos3 (x)
x 0		x x +1

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

	x <	)	;
tg(x) ,	x <	4	;
. -( (!# *+ " +( "2 ,: F (x) =		4
		)
	x - 4
sin(x),	x - 4

7. < #8 y/ 5% #6 (. ' +( "2 8:

a) y = 3(sin3 (2x + 3) 2					); b) y = x arcsin(2x) + ln(		)
a) y = 3(sin3 (2x + 3) 2				x	); b) y = x arcsin(2x) + ln(	x	)
	3x
c) y =	3x	63	2 + x	d ) y = (sin(2x)) x
c) y =		63	2 + x	d ) y = (sin(2x)) x
3	2 + x

8.<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = x + x3 ! 2 $ #-6- 2 6 @ x = 1 .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

a) lim tg(x) sin(x)		;	b) limln(x) ln(1 x)
x 0	x sin(x)		x 0

										43
								=11
	2	1	1		1		4	1	1		1 0 4			x	1		1	1	2
	2	1	1		1		4	1	1		1 0 4			x		3	2	1	1
	1						5	6	4			2	1 5	1		3	2	1	1
A =	1	5 1		B =	1	C =	5	6	4		D =	2	1 5	X = x2	F =	4	3	2	1
	3	2					9	7	3			3	1 9			4	3	2	1
	3	2	4		3		9	7	3			3	1 9	x3		1	0	1	5
																1	0	1	5

1.< #8 G = (C D) A + 2C ;

2.$!’%$# /# & & ! % % AY = C ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

d )

lim	1 3x5
	+ 7x2 + 3
x x5
lim 1 cos(5x)		,
x 0	3x2

	1+ x	1 x				1	6
, b) lim			,	c) lim
	3x						x2 9
x 0				x 3	x 3

e) lim x + 3 3x

x x 2

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

3x + 1 ,	x 1;
. -( (!# *+ " +( "2 ,: F(x) =	x > 1
x2 ,	x > 1
7. < #8 y/ 5% #6 (. ' +( "2 8:

a) y = 3 x4 + 5x 4(5x 1)3 ; b) y = x arctg(2x) + ln(x)

c) y =	1+ tg(2x)	63		d ) y = (2x 1)x
			x
	1 tg(2x)

8.<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = 2 + x x3 ! 2 . & -

( $ ! 66@ Oy .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

	ex 1		1
a) lim		;	b) lim(e2 x + x)
				x
	sin(2x)
x 0			x 0

											44
										=12
	1		3 2			1		1 1			7		1		3	1		x		1	1	7
	1		3 2			1		1 1			7		1		3	1		x
A =		1 2		1	B =	1	C =		3	2	18	D =		1	1	1	X =	x1	F =	3	2	18
																		2		4	3	25
		3	5	3					4	3	25			2	1					4	3	25
		3	5	3		1			4	3	25			2	1	1		x3		1	0	4
																				1	0	4

1.< #8 G = 3C 2 A(C D) ;

2.$!’%$# /# & & ! % % AY = C ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

+ 3x 7

2 + x 3

a) lim

, b) lim

, c) lim

+ x 1

x 7

+ x 2

x 7

x 2 x

d ) lim	arctg(5x)		2x 1	x
		, e) lim	2x + 1

x 0 arcsin(3x)		x

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

			1	x		x < 0;
. -( (!# *+ " +( "2 ,:			2		,	x < 0;
. -( (!# *+ " +( "2 ,:	F (x) =		2
		4 x,				x - 0
		4 x,				x - 0

7.< #8 y/ 5% #6 (. ' +( "2 8:

a) y = x2 x4 + 5 ; b) y = arctg 3 (2x + x5 ) + ln(x)

8.<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = e1 x2 ! 2 6 #-62 - 6 @ x = 1 .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

	1		1			3
							2
a) lim					;	b) lim(cos(2x)) x
	2			2
		(x)	x
x 0 sin						x 0

										45
								=13
	2	3	1		5		2	1 0			1 2 3		x	1		0	1	1
	2	3	1		5		2	1 0			1 2 3		x		2	1	6	4
					1		3	6	7			2 1 0	1		2	1	6	4
A =	3 2 1			B =	1	C =	3	6	7		D =	2 1 0	X = x2	F =	3	1	7	3
	1	2			2		5	1	1			3 0 1			3	1	7	3
	1	2	3		2		5	1	1			3 0 1	x3		4	1	8	2
															4	1	8	2

1.< #8 G = 2A + 3C CD ;

2.$!’%$# /# & & ! % %YD = C ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

lim

1 5x + 3x2

, b) lim

c) lim

5x + 6

x3 + 1

8x + 15

x 1

x 3

4x + 1

5 x

1 cos(3x)

d )

lim

, e) lim

x 0

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #


		x ,	x 4;
. -( (!# *+ " +( "2 ,: F(x) =		x ,	x 4;
	1,		x > 4
7. < #8 y/ 5% #6 (. ' +( "2 8:

			1			2

a) y =							( x) + ln( x)
a) y =	x5 arctg			; b)		y = e1+cos	( x) + ln( x)
			x

c) y =		1+ x2				d ) y = (x)arcsin( x)
c) y =		1+ x2	63		sin6 (x)	d ) y = (x)arcsin( x)
		1 x2

8.<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = x2 + 8x 32 ! 2 $

#-62 6 @ x = 4 .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

a) lim x ln(x);		+	3	x
a) lim x ln(x);	b) lim 1	+
x 0	x 0		x

										46
									=14
	1	1	2		1		1	7	2		7	1	11	x	1		2	3	4
	1	1	2		1		1	7	2		7	1	11	x		0	1	1	1
	2	4	0				3	6	3		2	0	3	1		0	1	1	1
A =	2	4	0	B =	3	C =	3	6	3	D =	2	0	3	X = x2	F =	1	6	7	8
	1	2	3				6	6 4			1 4		6			1	6	7	8
	1	2	3		1		6	6 4			1 4		6	x3		1	4	3	2
																1	4	3	2

1.< #8 G = 3D 2A(C D) ;

2.$!’%$# /# & & ! % %YA = C ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

lim

9x4 3x 5

, b) lim

3x + 2

, c) lim

x5 + 2x2

4x + 3

x 1

x 0

1+ 3x 1

d )

lim

e) lim(1+ 2x)

x 0

arctg(3x)

x 0

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

ln(x) ,		0 < x 1;
. -( (!# *+ " +( "2 ,: F (x) =	2x + 1,	x > 1

7. < #8 y/ 5% #6 (. ' +( "2 8:

a) y = arcsin( 1 x3 );

b) y = sin(x) 3

+ ln4 (

)

c) y =

2 + x

d ) y = (tg(x))x

3 x2

+ 3x + 5

cos(x)

<#. 6# & ! % % , # &/#5

*+ "# +( "2 , y =

! 2 . & ( $

!66@ Ox .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

a) lim tg(x) 1		;	b) lim(x)sin( 2 x)
x 4	sin(4x)		x 0
)			x 0

											47
										=15
	3	2	1		2		1	3	1		11 3	6		x		1	5	9	8
	3	2	1		2		1	3	1		11 3	6		x		1	3	5	2
	2	3	1				2	1			7 2	8	X	1		1	3	5	2
A =	2	3	1	B =	1	C =	2	1	1	D =	7 2	8	X	= x2	F =	1	4	7	5
	2	1	3				0	2			1 0	0				1	4	7	5
	2	1	3		3		0	2	1		1 0	0		x3		0	1	2	3
																0	1	2	3

1.< #8 G = 2AC 3(C + D) ;

2.$!’%$# /# & & ! % %YD = C ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

+ 3x +1

lim

2x2

, b)

lim

x2 9

, c) lim

1 1 x2

5x2

x 1

x2 2x 3

2x2

x 3

x 0

d )

lim

cos(4x) cos3 (4x)

3x +1

2 x+1

5x2

e) lim

3x 1

x 0

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

					2x ,		x 0;
	. -( (!# *+ " +( "2 ,:				F(x) = 2 x2	,	x > 0

7.	< #8 y/ 5% #6 (. ' +( "2 8:
	a) y = 3x arccos(2x +1);			b)	y = tg3 (3x) cos
	a) y = 3x arccos(2x +1);			b)	y = tg3 (3x) cos		2x +1
	c) y = 3x	2 + 2 3			y = (5x)ctg ( x)
		2 + 2 3	x2 + 5	d)
		ln x		d)
		ln x
8.	<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = e2 x ! 2 . & ( $

!66@ Oy .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

a) lim	1 cos(2x)	;	b) lim x ln(x)
x 0	3x2		x 0

										48
									=16
	2	1 1			4		1	4	1	5 4 3		x	1		2	3	4
	2	1 1			4		1	4	1	5 4 3		x		0	1	1	1
	4	1	2		1		2	6			X	1		0	1	1	1
A =	4	1	2	B =	1	C =	2	6	1	D = 10 9 8	X	= x2	F =	4	5	9	13
	1	1	1		2		3							4	5	9	13
	1	1	1		2		3	3 1		7 6 5		x3		1	6	7	8
														1	6	7	8

1.< #8 G = CD 3(C + A) ;

2.$!’%$# /# & & ! % % AY = C ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

lim

3 + x + 5x7

, b) lim

+ 6x + 8

c) lim

1+ 3x

1 2x

x3 + 8

x x2

x x7 12x3 +1

x 2

x 0

x2ctg(2x)

x + 3

x+4

d )

lim

e) lim

sin(3x)

x 0

x x + 5

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

tg(x),		x < ) ;
. -( (!# *+ " +( "2 ,: F (x) =	x,	x - )
1

7. < #8 y/ 5% #6 (. ' +( "2 8:


	a) y = e2 x (x4 +		x	+ 2x); b) y = tg3 (3x + x2 ) + arccos		x
	c) y =	x4 + cos(x)			d ) y = (ln(x))tg ( x)
	c) y =	sin2 (3x)			d ) y = (ln(x))tg ( x)
		sin2 (3x)
8.	<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = ln(x) ! 2 . & (

$! 66@ Ox .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

a) lim	x arctg(x)	;	b) lim xctg()x)
	x3
x 0			x 0

									49
								=17
3 3 2				2		1	5	6	1 0 4			x	4		5	9
3 3 2				2		1	5	6	1 0 4			x		1	6	7
	1	1 2		2		1	9	7		2	1 5	1		1	6	7
A =	1	1 2	B =	2	C =	1	9	7	D =	2	1 5	X = x2	F =	0	1	1
	3	2 1		1		1	13 8			3	1 9			0	1	1
	3	2 1		1		1	13 8			3	1 9	x3		1	4	3
														1	4	3

1.< #8 G = AD 3(C A) ;

2.$!’%$# /# & & ! % % DY = A ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

lim

2x7 + 5x2 + 3

, b) lim

x2 x 2

c) lim

1+ 3x2 1

1 8x7

x3 +1

x3 + x2

x 1

x 0

xtg(5x)

2 x x3

d )

lim

e) lim

1 cos(6x)

x 0

x x

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

		1	x < 0;
. -( (!# *+ " +( "2 ,:

	F (x) = x 1,
	1	+ x,	x - 0

7.< #8 y/ 5% #6 (. ' +( "2 8:

a) y = e

b) y = ctg

) + arcsin

cos

;

y =

1 3x2

d) y = (tg(7x))x

ln(3 x)

8.<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = x4 + 3x2 16 ! 2

. & ( $ .#- 5 @ y = 3x2 .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

a) lim xctg(x) 1		;	b) lim x2 ln(x)
x 0	x2		x 0

											50
										=18
	2	1	1		1		3	2	18		1 3 6		x	1		6	3	0
	2	1	1		1		3	2	18		1 3 6		x		4 0		12 12
	2	1	0				4	3	25			1 1 1	1		4 0		12 12
A =	2	1	0	B =	0	C =	4	3	25		D =	1 1 1	X = x2	F =	1	2 3		4
	1	1 1					1	0	4			2 3 4			1	2 3		4
	1	1 1			3		1	0	4			2 3 4	x3		3	2	9	8
															3	2	9	8

1.< #8 G = 31 A(C D) ;

2.$!’%$# /# & & ! % % DY = A ;

3.$!’%$# 6 6 /( AX = B , . .! 5( / / / K#(66#;

4.< #8 * /# & 2 F :

5.< #8 * 2 :

d )

lim	5x9 +1	, b) lim			x3 + 4x +16	, c) lim	2x 1	5
	3x 7x9				3x2 + 4x 4		x 3
x		x 2				x 3
lim(1 cos(5x))ctg			2			10x 3 5 x
				(3x), e) lim
x 0					x	10x 1

6.65 +( "2 @ # . & &! 6 7, $ #8 " & $& !( ! %! , '#" & #

. -( (!# *+ " +( "2 ,:

F (x) =

sin(x),

x 0;

x > 0

7. < #8 y/ 5% #6 (. ' +( "2 8:

cos

y = 4sin

a) y = e

+ cos

;

(10x) ln(1

2x)

c) y =

5tg(x)

d ) y = (tg(x))x2

1 arccos(x)

8.<#. 6# & ! % % , # &/#5 *+ "# +( "2 , y = x 1+ 1 ! 2 $ #-62 -

6 @ x = 0 .

9.& 6 (@ 67 .! 5 / . #5% $ #8 #6 (. * 2 :

	e3x 1		)x
a) lim		; b) limsin(x 1)tg
a) lim	arcsin(3x)	; b) limsin(x 1)tg
x 0	arcsin(3x)	x 1		2

<<< < Предыдущая 1 2 3 45 / 65 6 > Следующая >>>

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											44
										=12
	1		3 2			1		1 1			7		1		3	1		x		1	1	7
	1		3 2			1		1 1			7		1		3	1		x
A =		1 2		1	B =	1	C =		3	2	18	D =		1	1	1	X =	x1	F =	3	2	18
																		2		4	3	25
		3	5	3					4	3	25			2	1					4	3	25
		3	5	3		1			4	3	25			2	1	1		x3		1	0	4
																				1	0	4

											44
										=12
	1		3 2			1		1 1			7		1		3	1		x		1	1	7
	1		3 2			1		1 1			7		1		3	1		x
A =		1 2		1	B =	1	C =		3	2	18	D =		1	1	1	X =	x1	F =	3	2	18
																		2		4	3	25
		3	5	3					4	3	25			2	1					4	3	25
		3	5	3		1			4	3	25			2	1	1		x3		1	0	4
																				1	0	4

											44
										=12
	1		3 2			1		1 1			7		1		3	1		x		1	1	7
	1		3 2			1		1 1			7		1		3	1		x
A =		1 2		1	B =	1	C =		3	2	18	D =		1	1	1	X =	x1	F =	3	2	18
																		2		4	3	25
		3	5	3					4	3	25			2	1					4	3	25
		3	5	3		1			4	3	25			2	1	1		x3		1	0	4
																				1	0	4