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Пензенский Государственный Университет Архитектуры и Строительства

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<<< < Предыдущая 1 2 3 4 5 6 7 8 9 1011 / 1411 12 13 14 > Следующая >>>

III

Вариант 21

lim 2x33 7x2 2 x 3x 4x 3

lim

3x5 4x2 1

2x3 3x2 x

lim

x2 x 6

x 3 2x2 x 21

lim

3x2 x 2

3x2 4x 1

x 1

lim

x 10

4 x

2x2 x 21

x 3

lim

1 3x2

x2 x

x 1

lim

x2 3x4

x 0

lim

1 cos3x

x2 5x3

x 0

lim

n 3

2n 4

n 2

lim

3x 10

2 x 5

2 3x

lim

2x 3

x 2

lim

x 2

2x 3

2x 1

lim 1 4x x4 x x 3x2 2x4

lim

x3 x 1 3

x x 1 4 x4

lim

x2 x

lim

2x2 5x 7

3x2 x

x 1

lim

x2 x 12

4 x

x 3

lim

x2 4

1 4x 3

x 2

lim

cos x cos5 x

5x3 x2

x 0

lim

arctg2x

x 0

5x 3x2

lim

x x 1

lim 3 2x

1 x

x 1

lim

ln 3 2x

1 x

x 1

101

III

Вариант 22

x 1 3 x 1 3 lim 1 2 1 2

x x x

lim 3x3 5x2 2 x 2x3 5x2 x

lim x22 2x 15 x 5 2x 7x 15

lim		2x2 9x 4
			x2 x 20
x 4
lim	4 3x			4 3x
			7x
x 0
	lim		5x 1 4
			x 3
	x 3
	lim arctg3x
	x 0 5x x2
	lim cos3x 1
	x 0		x tg2x

lim n 4 3n 3 n n 2

lim 2 3x x x 0 2 5x

lim 3x 2 ln 2x 1 ln 2x 1

lim x2 ln x2 5 ln x2 5

lim 4x4 x 1

x x2 3x 5

lim 3x3 4x 6 x 3x5 6x 4

lim 3x22 5x 2 x 1 x 4x 3

	lim	x2 3x 2
	lim	2x2 5x 2
	x 2	2x2 5x 2

lim

5x x

x 5

lim

5 x

x 0

lim

1 cos 2x

tg3x 3x4

x 0

lim arcsin 2x

x 0

3x 4x2

x 3

lim

2 x

1 x

x 1

lim

x x 2 x

102

III

		Вариант 23
lim	x 1 3	x 1 3
lim	x3	3x
x	x3	3x

lim 2x4 5x2 3 x 5x4 2x2 4x

lim x2 x 12

x 4 x2 2x 8

lim x2 x 12

x 3 x2 5x 6

	lim	x 3
	lim	4x 3 3
	x 3	4x 3 3

lim			9 x 3
			x2 x
x 0
lim	cos x cos3 x
		x tg2x x2
x 0
lim		tg2 4x 7x3
			x sin 3x
x 0

lim n 5 2n 1 n n 5

lim 2n 3 n 2 n 2n 10

lim x 2 ln 2x 3 ln 2x 4

lim 2x 1 ln x 3 ln x 2

lim 3x3 3x 5 x 3x2 2x 4


lim		4x4 2x2 5
			5x5 x 3
x
lim			2x2 x 3
			x2 x 2
x 1
lim		3x2 10x 3
			x2 2x 3
x 3
lim			x 2
			4x 1 3
x 2
lim	3 x			3 x

x 0			5x

lim x sin 2x ctg2 3x
x 0
lim	1 cos 4x
lim
x 0 x sin 3x 3x3
		1
lim	1			3 x


x 0	x 1
				3 x
lim 2x 1			x 1
x 1
lim	x2 1 x
x

103

III

Вариант 24


lim	n 1 3 (n 1)3
			n3 1
n
lim			3x2	2x 1
				x 2
x 5x2
lim			2x2 3x 2
			x2 3x 2
x 2
lim		3x2 10x 3
			x2 2x 3
x 3
lim			3x 10 4
			x 2
x 2
lim			x 7
			2x 11 5
x 7

lim x sin 2x ctg2 5x

x 0

lim1 cos5x x 0 x tg2x

lim n 6 3n 5 n n 2

lim x 2 x 4 x x 4

lim 3 x ln 1 x ln 2 x

lim 3x ln x ln 2 x

lim x7 2 7x5 9x x 2x 5x 3

lim 6x3 2x 3 x 8x4 5x 7

lim x2 x 12

x 3 x2 5x 6

lim x2 x 12

x 4 x2 2x 8

lim

1 3x

1 2x

x x2

x 0

lim

x 3

3x x

x 3

lim

5x x2

x 0 arcsin 3x

lim

sin2

3x ctg2x

x x2

x 0

2 x

lim 10 3x

x 3

5 x

lim

3x 2

x2 1

x 1

lim

x 1

1 x

104

III

Вариант 25

lim		2x 1 2 x 1 2
				x2 x 1
x
	lim		5x5 3x2		1
			3x5 x3 5x
	x
	lim		3x2 14x 5
				x2 6x 5
	x 5
	lim			x2 3x 2
				2x2 5x 2
		x 2
lim				x 12	4 x
				x2 2x 8
x 4
lim		1 2x x2 1 x
				x
x 0

limsin 5x ctg3x

x 0

lim 5x 7x3 x 0 arctg6x

lim n 4 9n 6 n n 5

lim x 4 5x 1

x x

lim x 4 ln 2 3x ln 5 3x

lim		1			6

			x	2	9
x 3	x 3

lim

5x3 x 1

3x2 2x 5

lim

5x6 5x2

4x7 4x 5

lim

3x2 4x 1

x2 3x 2

x 1

lim

2x2 9x 4

x2 x 20

x 4

lim

x 1

x2 1

x 1

lim

x 13 2

x 1

x2 9

x 3

lim

1 cos 4x

x 0

x sin 2x

lim

1 cos10x

x tg2x x3

x 0

2 x

lim 2x 5

x 3

lim 7 6x

3 x 3

x 1

lim

4 x

2 2

1 x

105

III

			Вариант 26
lim	n 2	2	(n 2)2
lim	n		3
n			2
n

lim 2x2 9x 3 x 7x2 2x 4

lim 2x2 5x 3

x 3 x2 5x 6


lim		2x2 5x 7
		3x2 x 2
x 1
lim		2 x		x 6
			x2 x 6
x 2
lim		x 8		12 x
			x 10
x 10
	lim		5x 4x2
			arctg3x
	x 0

lim x sin 5x ctg2 2x

x 0

lim

n 3

3n 2

lim 5 4x

x 1

x 2

lim

x 1

lim

4x2 7x 4 2x

lim 4x3 2x 1 x 3x2 2x3 2

lim 6x56 3x2 1

x 2x x 3

lim x22 2x 15 x 5 2x 7x 15

lim 3x2 x 2 x 1 3x2 4x 1

	lim	1 3x2 1
	lim	x3 x2
	x 0	x3 x2

lim	x 5				9 x
		x 2
x 2
		sin	1

	lim		x
			1
	x 0
		tg
				3x

lim x sin 2x x 0 1 cos2 x

lim 2x 1 2 x x 2x 1

lim 3x 8 x 3

x 3

lim 1 ln 1 x ln 1 x

x 0 2x

106

III

Вариант 27

3 n 2 (3 n)2 lim 3 2 3 2

n n n

lim 5x32 3x2 2 x 4x 2x 9

lim 2x2 11x 5 x 5 x2 7x 10

lim x22 x 6

x 3 x x 12

lim	x2 3x 2
	5 x	x 1
x 2
lim	x 3
	x 1	7 x
x 3
lim x ctg10x
x 0
lim	cos x cos3 x
	x sin 2x
x 0

lim n 7 3n n n 5

lim 3x 7 4 x2

x 2

lim x 4 ln 2x 7 ln 2x 3

lim x2 ln x2 1 ln x2 1

	lim	4 7x2 5x3
	lim	2 2x x3
	x	2 2x x3

2x4 3x

lim 3

x 4x 2x 7

lim x2 x 2

x 2 x2 x 6

lim 2x2 7x 4 x 4 2x2 13x 20

lim	x 6				2 x
lim			x 2
x 2			x 2
lim			x 6
lim	x		5	7 x
x 6	x		5	7 x
	lim arctg8x
	x 0 x3 4x
lim			1 cos8x
x 0		1 cos 4x
			3 2n n 2
lim
n			4 2n
					x
lim 3x 2					x 1
x 1
2		x3 2				x3 2
lim x3		x3 2				x3 2
x

107

III

Вариант 28

6 n 2 (6 n)2 lim 6 2 1 2

n n n

lim x5 2 2x3 9x x 2x 5x 6

lim	2x2	9x 18
	x2	7x 6
x 6

	lim		x2		x 2
			2x	2 x 1
	x 1
lim		3 2x				x 4
		3x2 4x 1
x 1
		lim		x 2
				2x 2
		x 2
					x


limsin2					2
					x2 4x3
x 0

lim x sin 3x ctg2 2x

x 0

lim n 3 n 5 n n 2

x 9

lim x 11 x 10

x 10

lim x 5 ln 2x 3 ln 2x 3

lim x 3 ln x 2 ln x 3

	lim	4 5x2 3x5
	lim	8 6x x5
	x	8 6x x5

lim 2x2 2x 5 x 4x4 3x 6


lim	x2 10x 21
	x2 8x 15
x 3
lim	2x2 3x 1
	2x2 5x 3
x 1
lim	x 4
	5x 5 5
x 4
lim	x 1	5 x
	x 3
x 3

lim x2 7x3 x 0 1 cos6x

lim1 cos 4x x 0 1 cos8x

	n 2		n 4
	lim	4
	n n	4
				x2
	lim 2x 3			x 2
	x 2
lim	3x 4	x2 6 x
x

108

III

Вариант 29

lim

3 4x

3 3 x 3 3

x x

lim

5x3 3x 7

4x2 2x 8

lim

3x2 17x 28

x2 9x 14

x 7

lim

3x2 14x 5

x2 2x 15

x 5

lim

1 3x

6 2x

2 x 5

x 5

lim

x 1

x 2

4 x

x 1

lim

arctg11x 2x2

7x x3

x 0

lim

x tg5x

1 cos 4x

x 0

lim

n 6

n 4

3 x

lim

2x 5

x 3

lim

1 4x

3x 2

lim

x 1

lim 3x44 2x2 7 x 9x 3x 5

2x5 7x4

lim 3x6 6x2 1

lim x22 7x 10 x 2 2x 9x 10

lim x2 6x 5

x 5 x2 4x 5

lim	3 x	3 x
	5x
x 0
lim	x 5	7 x
	x 6
x 6

x sin x lim 2 x 0 1 cos x

	lim	cos x cos5 x
	lim	x2 x5
	x 0	x2 x5

lim 3n 2 3n 2 n 3n 1

			x2
lim	3x 5		x 2
x 2
lim x		3 x2	x
x

109

III

Вариант 30


lim	x 2			3 x 2 3
		x4		2x2 1
x
lim			3x 14x3
			2x 7x2
x 1

lim 2x22 13x 7 x 7 x 9x 14

lim x2 4x 12 x 6 x2 8x 12

lim	3x2 4x 1
	x 3 5 3x
x 1
lim		x
	x 7		7 x
x 0
lim cos3x cos5x
x 0		x2 6x3
lim		x2 ctg5x
		sin 2x
x 0

lim

n 7

5n 3

n 1

3 x 5

lim

4x 9

x 2

2x 3

x 3

lim

2x2 1

2x 1

lim

x 2x2

5x4

2 3x2

lim

3x2 7x3

x 4x3 10x4 x5

lim

3x2 8x 3

x2 x 6

x 3

lim

2x2 7x 30

3x2 20x 12

x 6

lim

1 3x2

x2 x

x 1

lim

x 3

5 x

x 4

lim

1 cos 4x

x 0

2x tgx

lim

sin2x 7x3

arcsin 3x

x 0

lim

2n 5

lim

7 3x

2 x 4

x 2

lim x

x 3

x 4

110

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