, Y. y ÎY xÎX. , * * D(*), D(*), d(*), d(*).
. , :
1) y ÎY xÎX;
2) ;
3) .
, .
y ÎY ÎY, . , e > 0 d = d(e) > 0, *, D(*) < d *, D(*) < e. , , .
.
1.5. x2 + px + q = 0. q. ,
. (1.1)
, , , .
1.6. . , 1, det A = 0 . , 22 e ¹ 0 , 2.
. , , , . , . , , , e. . , ? .
. , , , .
1.7. :
|
|
.
: = 12.1; = 9.09. . : = 1; = 1. , , , .. .
.
. .
D(*) £ nD ×D(*),
nD .
d(*) £ nd × d(*),
nd .
n >> 1 ( ). , n = ¥.
1.8. .
f*(x) , .
D(I*) = | I I*| = £ (b a) ×D(f*).
, -, , .. e > 0 D(I*) < e , D(f*) < e / (b a).
-, , nD = (b a).
. , :
1) xÎX y ÎY;
2) ;
3) .
, . .
, .
1.9. , d = p2 4q ³ 0. (1.1), . , d*, p* q* , d 0. . (1.1) d max(d; 0), .
, ( ).
, .. .
|
|
1.10. n n = 1, 2, yn = anyn1 + bn, 0 . *n , yn y*n= an(yn1 y*n1). , D(y*n) = |an|×D(y*n1). | an | < 1 , D(y*n) £ D(y*n1) n. | an | ³ q >1 , D(y*n) ³ qn ×D(y*0) n ¥.
1.11. n = 1, 2,. , In = n In1 1 (1.2)
I0 = e 1 1.71828, .
1.10. , (1.2) , .. an = n >1. , 6- , I*10 = 6.536, , , , .
, . (1.2)
(1.3)
, , n = 54, I54 = 0. , D(I*54) £ 0.05. I53 n , .. 54 , I52 53 .. n = 50, 1 7- . , (1.3), , .
, . , , , . 1.9 1.11 . . , . , 1.6 1.7 , , .
1. () = |x| + b×|x 2|, b 1. ?
2. .
3. 1.7 .