Επαλ απο mathematica

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    05-Sep-2014
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1 1 1 5 x 11 = , 8,12,14 11. 1. 10 2. . 3. S 2 = . 4. . 2 2 50 . ix 2 5 4 = , : 1. 2. 3. 16 4. 14 3 3 2,6,7, 3,7, x 6 1. x 11 = 2. , 0M R . 3. 0 03R 2 M M = . 4. , . 2 4 4 : 4,5,7,9,8,5,4 1. . 2. , 9 3. () , . 5 5 , 6,7,12,8,, ( < ) 8. . 1. : 7, 8 = = 7, 8 = = 2. . 3. . 6 6 50 , 1.120. 50 , 20 30 . 1. 1.000, . , , 800 2. 1.000, ; 3 7 7 1. 2. 3. 4. 2 5. 6. . 8 8 50 . 1. 2. 3. 4. 12 5. 4 9 9 50 . , : 1. . 3 = : 2. . 3. . 4. 3 5. 1 1 10 0 ( ix ) 1. c 4 = 2. 40 = 3. 4. 5. 5 1 11 1 , 67,5 1. , : . 52,8 , . 55,72, . 58,7. 2. . 1 12 2 x 4 = . 1. 2 = , : 2. 3. 4. , 6 1 13 3 , . : 1. . 2. i i i i , N ,f ,F% 3. , . 4. % 5. . 6. 6 . 7. , : 4 1.300 oi 4 , 8 1.600. 8 1.800 1 14 4 ( ) . 5 . 7 1. 2. i i i i , N ,f ,F% 3. . 4. 30 . 1 15 5 . 1. 2. x 5 = 3. 2S x = 4. . 22, 24 5 ~ 8 1 16 6 . 1. oM < oM , 2. 2 xS2= 2S , x 3. 4. 4 5 5, 21,41 2 ~ 5 10. 1 17 7 400 110 . 1. 3 = . 2. . : 9 110 120 , 120 140 100 , 140 160 200 160 180 500 . 3. , 3 157,144 166 , , . 1 18 8 : O 0,1, 2, 3, 4 . 10 1 . 2 . 2 30 . 1x 0 = , 036 4 10% 1. v , if . 2. . 3. . 10 1 19 9 ( ) 270 : 1. 2. 72 3. 72 4. 66 ; 5. 150 3 1, 5 , ; 2 20 0 60 . 1. . 11 2. . 3. , 10 3 , 2 . ; 2 21 1 : 1. ( ) f x 2x 3 = f (0) f (1) f ( 1) = 2. ( ) 2x g x , x 24x 8+= = + ( ) ( )x 1 x 12limg x 3limg x 5 = 3. ( ) 3x 1, x 0h x3 2lnx , x 0 + s = > 3h( 2) 2h(e) 4 5 = 2 22 2 : 33 2x 1x 3x 2A limx x x 1 += + 2 x 2x 2 xB lim3 x 5 + += + 12 2 23 3 : 3x 23 x 2 2 5x 1A lim4x 15x 2+ = ( ) ( )2 x x x2x 12x e 3xe eB limx f x xf x= + f M(1, 2012) 2 24 4 f (x) x 1 1 = + g(x) x 1 3 = + 1. f g 2. 2x 3f (x) 1limx 5x 6 | | | +\ . 3. 3x 22g(x) 4xlim8 x | | |\ . 4. A f(3) 2g(5) f(0) = + 2 25 5 23 22x x 3, x 2x 2x 4x 8x , x 2f (x)( x 12 4), x 2x 2 + < + == + > 1. f M( 1,1) , 4 = 13 4 = 2. x 2limf (x) 3. x 2limf (x)+ 4. , R e f 0x 2 = 2 26 6 1. 22x 3x 9lim2x 9x 9| | | +\ . 2. 3 22x 2x 3x 4limx 4x 4| | + | +\ . 3. 2x 1x 3 2limx 1| |+ | |\ . 4. 2x 1x 2 3limx 1 x x+ | | | \ . 5. x 2x 1 3 xlimx 2 2| | | |+ \ . 6. 32 x 2x 8limx 5 3| | |+ \ . 7. 4 3 22x 1x 5x 3x 1limx x| | + + + |+\ . 2 27 7 22x 5x 6f (x)x x+ +=+ 1. 2. ( )x 1lim x 5 2 f (x) (+ 3. 2x 2f (x)limx 4 | | |\ . f (x) f (1), x (1, )x 1 g(x), , x 1 e + = = 14 4. R e g 0x 1 = 2 28 8 , : 1. ( ) f x lnx 2 = + x 0 > f (x) (1,6) (e, 3) 2. ( ) 2x 2 , x 3g x 2 , x 1 3 = = = g(3) 2g( 1) 4 = = 3. ( ) x 2 3 , 2 x 8h x x 2 , x 9 + s = h(x) 2(2, 2) + (9,11) 2 29 9 222x 2x 1 1, x 0x , x 0f (x)x x , x 0 + + < + == + > 1. x 0limf (x) 2. x 0limf (x)+ 3. , R e f 0x 0 = 15 4. , R e , A 2f(0) f(1) f( 1) = + 3 30 0 f : 23 22x 1, x 1x 1f (x) x 2 , 1 x 1x 6x 7x, x 1x x < = + s s + > , R e .: 1. x 1 x 1lim f (x), lim f (x) + 2. x 1 x 1limf (x), limf (x)+ 3. , f R 3 31 1 1. : 16 ) x 4lim f (x)+ = ) x 2lim f (x) = ) x 2lim f (x)+ = ) x 0limf (x)+ = ) x 0limf (x) = ) x 2limf (x) = ) x 2limf (x)+ = ) x 4limf (x) =2. f 3. f 4. f 3 32 2 ( )22x x 3 , x 13 6,, x 1f xx 2 xx 1 + < = = ++ > , R e 1. ( )x 1lim f x 2. ( )x 1lim f x+ 3. ( )x 1limf x 4. 2 = , f ox 1 = 17 3 33 3 ( )( )22 x 3 2, 3 x 12x 25f x 2 , x 182x 3x 1, x 1x x + s < = + = + > ,e . 1. ( )x 1limf x . 2. ( )x 1limf x+. 3. ( )x 1limf x. 4. 8 = , f 0x 1 = . 5. 8 = , 2K f ( 2) f (2) = 3 34 4 ( ) 2x 3 , x f x4x 1, x s = > ( ) ( ) 23f x , x 2g x4 3 , x 2 == = e . 1. ( )x limf x 2. ( )x limf x+ 3. f 1x = . 1 = : 4. ( )x 2limg x 5. g 2x 2 = 18 3 35 5 ( ) ( )x 53e 2x , x 5f x2ln x 4 3 2, x 5 s= + + > ( ) ( )2 xln x e 2011 , x 0g x3 , x 0 + + == = , R e . 1. ( )x 5limf x. 2. ( )x 5limf x+. 3. ( )x 0limg x. 4. f 1x 5 = g 2x 0 = . 5. 4 = 2 = , ( ) ( ) ( )2K 2f 0 3f e 4 g 0 2012 = + . 3 36 6 3 222x 5x 6x, x 3x 3xf (x) x 11 , x 3 + > += s 1. x 3limf (x) x 3limf (x)+ 2. R e f 0x 3 = 3. (2) , 2 2x 5x ( 2)x 5limx 5 + + 19 3 37 7 25x 10, x 2x 1 x 7f (x)x 5x 4 , x 2 > + += + s 1. x 2limf (x) x 2limf (x)+ 2. R e f R 3. 2 = x 1f (x) f (1)limx 1 | | |\ . 3 38 8 2f (x) 9 x = x 2g(x)x 3= 1. f g 2. 2h(x) f (x)g(x) = 3. x 3limh(x) 4. x 5f (x) 2limx 5 | | |\ . 3 39 9 223 x , x 15x , x 1 x 1f (x), x 1x < = = = > 20 1. x 1lim f (x) x 1lim f (x)+ 2. x 1limf (x) x 1limf (x)+ 3. , R e f R 4. 2 = 5 = , 1A f (0) f (2) 4f ( )2= + 4 40 0 ( ) f x 5x 10, x 2 = + > ( ) 2g x x 3 = + ( ) f 3 h 5h 25,h 5 + = + > ( ) 2g 3 h h 6h 12 + = + + 1. ( ) ( )h 0f 3 h f 3A limh+ = ( ) ( )h 0g 3 h g 3B limh+ = ( ) ( )( ) ( )h 0f 3 h f 3C limg 3 h g 3+ =+ ( ) ( )h 1f 3 h f 2D lim3h g(0)+ =+ 4 41 1 : 1. 2 x 3x 3f (x) x e x x lnx 20123 x= + 2. ( )( )2 2 4g(x) 4x 3x 2 2x 5x 2 e = + + 3. 22x 3xh(x) xln55x 20+= 4. 2xx 3xk(x) 3e= 21 4 42 2 1. 3 2x 5xf (x) 6x 23 2= + 2. 2 xg(x) x e ln3 = 3. lnxh(x)x= 4. xs(x) e x = 4 43 3 3 2f (x) 2x 3x 12x 3, x R = + e 1. f' f'' 2. x 2f (x)limx 2 2'+ x 1f (x) f (1)limx 1 3. f 4 44 4 3 2f (x) 2x x 12x 1, R, x R = + + + e e 1. f ( 2) f (1)' ' = , 3 = 3 = 2. N f