infi-07b-sol11_0 - 2007 11 " 20106 11 " 1...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2007 11 " 20106 11 " 1 (1 ) .2 - x 2 x - 1 x 1 , x 2 1 x - 1 0 2 x2 - 1 . x - 1 2 - x - 2-x- x -1 2 (2 ) x 2 2 - x 0 ,- ( ) .(3 ) (2 - x ) x - 1 x - 4 x + 4 x - 1 4 x 5 x 2 2 2 2 5 4 . ( - , - 1] [1, 5 ] : (3) - (2) ,(1) 4 . - 1 x 2 - 3 x + 1 1 , [ - 1,1] Arcsin x -1 x2 - 3x + 1 0 x2 - 3x + 2 . ,2 - 1 0 = x 2 - 3 x + 2 . ( -,1] [2, ) x 2 - 3 x + 1 1 x ( x - 3) 0 ,3 - 0 0 = x ( x - 3) . [0, 3] . ( ( -,1] [2, ) ) [0, 3] = [0,1] [2, 3] : - 2 (*) ( 2 x + x ) (1 - x ) > 0 . 3 x (1 - x ) > 0 : x = x x 0 . . x 0 . 0 < x < 1 . x (1 - x ) > 0 : x = - x x < 0 . 1 - x < 0 x < 0 . 0 < x < 1 : . tan x = tan x tan x 0 [0, ) - [ - , - ) . 2 2 . tan x 2 sin x : . - , sin x < 0 ( - , - ) - 2 1 2007 11 " 20106 . - , tan( - ) = sin( - ) = 0 - - cos x > 0 [0, ) - 2 tan x = sin x 2 sin x sin x 2 sin x cos x cos x - - sin x > 0 x 0 - , x = 0 - . 0 < x - cos x 1 1 2 cos x 3 2 . [0, ] {- } : 3 . tan x = - tan x tan x < 0 ( , ) - ( - , 0) 2 2 . - tan x 2 sin x : . - , sin x < 0 ( - , 0) - 2 cos x < 0 ( , ) - 2 - tan x = - sin x >0 sin x 2 sin x - sin x 2 sin x cos x - 1 2 cos x - 1 cos x 2 cos x . [ 23 , ) - . [0, ] [ 23 , ) {- } [ - , ] - : 3 3 b-a = b- a - a = b- a + -a 2 2 2 ( 2) (1) (2) (3) a a b- a + -a = b- a + a < + = a 2 2 2 2 2 2 - (1) - x = x ( 2) a a . a = = , (3) 2 2 2 4 (*) , x = x - x - .- 1 1 1 < x -1 < x - 1 < (i ) . 2 2 2 1 3 < x< (*) 1 2 2 . ,- 1 < x 2 9 9 7 9 (*) 4 < x + 3 < , < x + 3 < 2 2 2 2 2 2007 11 " 20106 . x+3 < 9 2 : x 0 (ii ) (*) 2 2 2 3- x 3 - x - 2 x (1) x + 2 x - 3 ( x - 1)( x + 3) (2) 1 1 x -1 x + 3 -1 = = = = 2 x 2x 2x 2x 2x - x = x - , ( - 1) - (1) . ab = a b (2) . 0 < < 1 2 , 1 x < 2 x > 1 (i ) x - 1 < 1 x - 1 < 2 2 . x+3 < 9 2 : .(**) .< 2 90 (*) 3- x 1 9 -1 = 1 x -1 x + 3 1 2 9 = 2 x 2 2 2x 2 2 9 1 = 1 , < : , 1 - 45 10 2 10 : ,( 0 < < 1 ) = 2 1 100 , , . , 2 (1) 3- x 9 9 1 x - 1 < -1 = < 2x 2 200 10 . x - 1 < 1 - (**)- (1) 2 . x 2 + sin x (*) x 2 - 1 x2 - 1 1 x2 - 1 x - 1 > = = 2 x + cos x 2 x + 1 2 x + 2 2 x + 1 2 : x > 2 . . , (*) : x > M , , M = 3000 . , x 2 + sin x x - 1 2000 > > = 1000 2 x + cos x 2 2 ,- M- : x 2 + sin x 2 x + cos x . (*)- 5 ("" or) . '- ' 3 2007 11 " 20106 . [ x ]2 = 4 [ x] = 2 2 x<3 or - 2 x < - 1 . [ x2 ] = 4 4 x2 < 5 2 x< 5 or - 5 < x -2 . . . 0 2 r < 2 - 2 x = 2[ x ] + 2 r . 0 r < 1 , x = [ x ] + r x . [2 x] = 2r < 1 2 [ x] 2 [ x ] + 1 2 r 1 . 0 r < 1 - n x = n + r 2 6 : , . . x R f ( x ) = 0 f f ( x ) = f ( f ( x )) = f (0) = 0 = f ( x ) : x R . R f , f (1) = 0 . . . f ( x) = f f ( x ) = f ( f ( x )) = f ( y ) : . f ( x ) = y x R =y . x = f ( x ) , x = y - ,-- f . , x R x = f ( x ) - : . f ( y ) = x - y R , f . x R . . . x = f ( y) = f f ( y ) = f ( f ( y )) = f ( x ) . , f ( x ) = x x R . f ( x ) < f ( y ) g ( x ) < g ( y ) : . x < y - x, y R . . , f ( x ) + g ( x ) < f ( y ) + g ( y ) - . ( f + g )( x ) < ( f + g )( y ) : . . . f ( x) = x g ( x) 0 , ( f + g )( x ) = f ( x ) .( 0 = g (0) < g (1) = 0 0 < 1 ) g 4 ...
View Full Document

This note was uploaded on 07/23/2009 for the course MATH. 04101 taught by Professor ישראלפרידמן during the Summer '06 term at The Open University.

Ask a homework question - tutors are online