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[НЕСОРТИРОВАННОЕ]

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Матан Лекции

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, %#/ 32 2. % & 7 * # $! # *

M (b - a)5 r2n £ 2880n4 .

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# &

			b																			a + b
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			a																			2
			a
+ 7# + 0	' y = x - c. &(
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#
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		b (x - a)(x - c)(x - b)dx =																	b - a									b - a
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																	y +				y y -										dy =
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		a								-			b-a							2									2
										-
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						b-a									(b - a)
															(b - a)
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					-
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	4		16		16									8				4							4
	4		16		16									8				4							4
# // ( / K, (	& + 3 %## 30, %

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, %#/ 32 2. % & 7 * # $! # *

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(R2

(x)- K (x - a)(x - c)(x - b))dx

R2 (x)- K (x - a)(x - c)(x - b)

dx £ b

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									b-a
b																- a b					- a
b										2					b
										2					b
(x - a)(x - c)2 (b - x)dx =												y +						y 2				- y dy =
(x - a)(x - c)2 (b - x)dx =												y +				2		y 2			2	- y dy =
a								-		b-a						2					2
								-
										2
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					2
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12	8					8					5		32							32			120
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( # |Dk| 0 Dk, |Dk| = (b - a)/n. .& 7 * r2n $! # *

0 [a, b] +!7 * !

& 7 * ' 2( #0 0 + Dk. 8 * 3 2 # 0+ /

' # %

b - a 5

M (b - a)5

r2n

= n

2880

2880n

k =1

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*! ( / * # + #/ # /

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# 1.

1. .* 0 # - 2 * +. #0 * ( 6#" 2 * + * ( 2# 0

a)A È ;

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c)A\B

2. .* 0 # - 2 * +. # #0 * ( 6#" 2 * + * ( 2 */ + 0

a)A È ;

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	3 2 # ?

a)X=[0,1];

b)X=[-1,1];

c)X=[-0.5,0.5];

d)X=[-1,-0.5] È [0,0.5]

5. .* 3 2 # f : X 5Y, Y=[0,1 ], 0 ( */ $' f (x) = x2 . / #" 2 * + X $ %#/ f /+ / */ +0 # ( 0 ) ! 3 2 #?

a)X=[0,1];

b)X=[-1,1];

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c)X=[-0.5,0.5];

d)X=[-1,-0.5] È [0,0.5]

6. .* 3 2 # f : X 5Y, X=[0,+=), Y=[0,+ = ] ,0 ( */ $' f (x) = x 2 . ' $' 0 ( */

3 2 # f -1 , 3 f ?

7. .* 3 2 #/ f : X5X, g : X5X, X=(-=,+=), 0 ( */ $# f(x)=x2 g(x)=sin x. .* # * 2 ! 3 2 #/ f o g # g o f .

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*! ( / * # + #/ # /

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# 2

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a)X = {(x1 , x2 ) : x1 Î–, x2 Î–}

b)X = {(x1 , x2 ) : x1 Î–, x2 Î—}

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2. .* X jk , j ÎÕ, k ÎÕ - *) ! 2 * +. 4 ( # *) ! 2 * +

¥¥

UU X jk .

j =1 k =1

3. .* 2 * + X * * # #0 +* " 3 * ) !" ( */ #) !" ( 3 '

x= 0.a1a2 ...an ...,

# 6#" + *+ 0 2 ## %#$ 9 # 8. 4 ( # 2 * + X *) !?

4.	.* X = {(x , x	) : x Î—	, x	Î—	} , &( —	= — Ç 0,1 . ;+ / / # 2 + X # —	0	+ 6 ! #?
	1 2	1 0	2	0	0	[ )	0

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a)sup( X UY ) = sup X + supY

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c)sup( X UY ) = max{sup X ,supY}

2. .* X # Y - & #) ! 2 * +, X Ì Y. #0 * ( 6#" * 7 #' * + ( #+

a)sup X £ supY

b)sup X ³ supY

c)sup X = -supY

3. .* X # Y - & #) ! 2 * +, X Ì Y. #0 * ( 6#" * 7 #' * + ( #+

a)inf X £ inf Y

b)inf X ³ inf Y

c)inf X = -inf Y

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8. .* X ={1, 12 , 13 ,..., 1n ,...} . ' # sup 2 # inf X.

326

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3.	.* limn®¥ xn	= l # limn®¥ yn = p,		l ¹ p	4 ( # * (#		/ * ( + * x1 , y1 , x2 , y2 ,..., xn , yn ,... " (/6 '/?
4.	.* limn®¥ xn	= limn®¥ yn	= l . 4 ( # * (#			/ * ( + * x1 , y1 , x2 , y2 ,..., xn , yn ,... " (/6 '/?

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n®¥ x

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= 0 ?

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.* * ( + * x1 , x2 ,..., xn ,... *" (# */, * ( + * y1 , y2 ,..., yn ,... *" (# */. + ( * 3/

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# 6

n®¥ xn

lim

n®¥ xn

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lim

n®¥ xn

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n®¥ xn

n®¥ yn

=1. #, )

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(xn + yn ) = 2;

lim

n®¥

(xn yn ) =1.

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n®¥

n®¥ xn

= limn®¥ yn

=1. #, )

lim

(xn

+ yn ) = 2;

lim

n®¥

(xn yn ) =1.

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n®¥

n®¥ xn

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a) lim (xn + yn ) = 0;

n®¥

b) lim (xn yn ) = -1.

n®¥

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329

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