= = = = 2 5 a a b b b a b c d = a + c b + d a b, c d =
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2 2 3 < < 2, 3 5 < < 2 3. x y y x x < y ( y > x) z x < y x + z < y + z z x < y, z > 0 xz < yz z x < y, z < 0 xz > yz x y x y x y ( y x) a b, c d a b < c d a b < a b c d a + c b + d < c d. a b < c d c d a b a b < a + c b + d a + c b + d a b a b < c d c d a b bc bd ad bd a + c b + d a b b(a + c) + d) a(b b(b + d) b(b + d) bc ad bd b(a + c) a(b + d) b(b + d) 2 > 0. bc ad > 0. ba + bc ab ad b(b + d) bc ad b(b + d) > 0.
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5 3 a b < c d c d a b bc ad bd bc ad bc ad bc ad a b c d > a b c d a b c d a + c b + d a b a b c d, a b c d c d a b c d 2 p q q b + d a b c d a b c d 2 a b < c d bc ad. a b a + c b + d b(a+c) a(b+d) bc dc a b < p q < c d p q a b < p q bp aq > 0 bp aq, p q < c d cq dp > 0 cq aq. bp aq d cq aq b q (bc ad)q (bp aq)d + (cq aq)b d + b. p q a + c b + d 4 x x p x x q 5
6 x p q p q x p q π π 7 3 x 2 x 0, x (x x 0 +. ) x 2 x 0 x x 0 x, x 0 x 2, x 2 x x 0 x 2 x 2 x x x 0 x 2 x x 0 < x < x 2 x 3 x 0 x 2 x 2 x x x 3 x 2 x x n x k (k < n) x x n+ x n+ x n x k x n x N N x x x n g x g x n x n x n x n x g x n+ x n x n 0 6
7 , x x [x] [x] [x] x < [x] + [2.3456] 2, [ 7.89] 8. x a m y m (m 0,, 2,... ) a 0 [x] y 0 x a 0, m [ ] a m+ y m y m+ y m a m a m, 0 < y m < (m ). y m a m+ + y m+ y n x a 0 + y 0 a 0 + a 0 + a + a 2 + a + y a a m + y m a m+ + y m+ a + a 2 + y 2 x a 0 + a + a 2 + a
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9 g g g + g 2 2 h + 2 a m y m + 2 c + 2d a + 2b a 2b (a + 2b)(a 2b) a 2 2b 2 x h + 2 a 0 2, y 0 ( 2 + ) 2, y 0 2 ( 2 )( 2 + ) 2 + h. ym 2, + 2 h, a m 2. y m h π a 0 3, y 0 π , , y 0 a 7, y , , a 2 5, y , , y y 2 a 3, y , , a 4 293,... y , , , p m x n 9
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