контрольная_2_ВведВ МатАнализЭЛЕКТР

1. xn

=

5n + 3

, A =

5

, = 10 2.

5 3n

3

3.

3

+ 1

)

lim

x

;

x

+ 1

x 1

4

2

+ 4

3

+ 5

x8 + 100

)

lim

x

x

;

x +

x2

+ x3 + 100x4

)

ln (1 + x + x2 )

lim

;

sin x

x 0

+)

lim

ln(1

+ sin 2 x)

;

(e2x 1)2

x 0

arctg 2x

,

x " 0,

2x 1

y =

4.

m,

x = 0;

xo = 0.

6.

)

2 1 x ,

x 1,

y =

x > 1;

x2 1,

1

')

y =

;

ln(x 1)

2. lim

5x 10

=

5

.

4 x2

4

x 2

1 +

2

1 +

1

')

lim

x

x

;

x 0

()

lim

sin (x 2 )

;

x 2

x2 4

5x2 + 2x + 1

5x

)

lim

;

2

5x

x

)

lim

ln (1 + 5 x)

;

x 0

5 1 + 2x 1

!)

lim

cos x cos 2 x

.

x 0

2 x sin (x

2x )

)

lim

3

9 x

2

;

x 1

2 x

1

4

x

+ 4 x3

+ 5

x3

)

lim

x

x

;

x +

x2

+ 50x3 + 100

)

lim

ln (2 2x + x2 )

;

x3

1

x 1

+)

lim

sin4 2x

;

(cos x 1)2

x 0

)

lim

sin 2x 1 x

;

x +0

2x

x2

4

y = x

3

8 , x " 2,

4.

m,

x = 2;

xo

= 2.

6.

1 +

1

1 +

1

') lim

2

x

x

;

x 0

()

lim

tg (x 5 )

;

x 5

x2 5x

)

lim

x

;

1 5x

x

)

lim

ln (1 + 9 x3 )

;

(3

1)3

x 0

1 + 2x

!)

lim

tg (ln (3x 5))

.

x 2

ex2 2 ex