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By Philip Ross

This primary complete survey of office layout for the recent century, this e-book captures rising issues and ideas in workplace structure and interiors all over the world. Written and researched via the authors of The artistic place of work, it advances the concept that of accelerating creativity in making plans and layout by means of exploring the hot office types which are constructing in accordance with fast organisational, social and technological switch. within the creation the authors talk about how the hot office of the twenty first century is already displaying assorted spatial, organizational and fabric features from the scientifically controlled, process-driven, mechanistic version of the 20 th century sleek place of work. this is often by means of 4 thematic chapters that illustrate the major new developments via forty five foreign case reviews.

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N 7! un , n 2 Z + For example, f2n + 1g generates the sequence 3, 5, 7, 9, 11, .... EXERCISE 2B 1 List the first five terms of the sequence: f2ng f2n + 3g a e f2n + 2g f2n + 11g b f c g f2n ¡ 1g f3n + 1g d h f2n ¡ 3g f4n ¡ 3g c f6 £ ( 12 )n g d f(¡2)n g 2 List the first five terms of the sequence: f2n g a f3 £ 2n g b 3 List the first five terms of the sequence f15 ¡ (¡2)n g. C ARITHMETIC SEQUENCES An arithmetic sequence is a sequence in which each term differs from the previous one by the same fixed number.

As the factors are ‘single’ the signs alternate. , x = 4. As ¡4(1)2 is < 0 we put a ¡ sign here. As the factor is ‘squared’ the signs do not change. 100 - x black x IB_HL-2ed 31 FUNCTIONS (Chapter 1) Example 9 x¡1 : 2x + 1 Draw a sign diagram for x¡1 2x + 1 is zero when x = 1 and undefined when x = ¡ 12 : + So, -\Qw_ 1 x¡1 = 2x + 1 For x = 10, x 9 21 >0 Since (x ¡ 1) and (2x + 1) are single factors the signs alternate. CDR Thursday, 12 July 2007 12:52:26 PM DAVID3 IB_HL-2ed 32 FUNCTIONS (Chapter 1) 2 Draw a d g j m sign diagrams for: (x + 4)(x ¡ 2) ¡(x + 1)(x ¡ 3) x2 ¡ 9 x2 ¡ 3x + 2 6 ¡ 16x ¡ 6x2 b e h k n x(x ¡ 3) (2x ¡ 1)(3 ¡ x) 4 ¡ x2 2 ¡ 8x2 ¡2x2 + 9x + 5 c f i l o 3 Draw sign diagrams for: a (x + 2)2 d ¡(x ¡ 4)2 g 4x2 ¡ 4x + 1 b e h (x ¡ 3)2 x2 ¡ 2x + 1 ¡x2 ¡ 6x ¡ 9 c f i 4 Draw sign diagrams for: x+2 a x¡1 x(x + 2) (5 ¡ x)(1 ¡ 2x) 5x ¡ x2 6x2 + x ¡ 2 ¡15x2 ¡ x + 2 ¡(x + 2)2 ¡x2 + 4x ¡ 4 ¡4x2 + 12x ¡ 9 b x x+3 c 2x + 3 4¡x d 4x ¡ 1 2¡x e 3x x¡2 f ¡8x 3¡x g (x ¡ 1)2 x h 4x (x + 1)2 i (x + 2)(x ¡ 1) 3¡x j x(x ¡ 1) 2¡x k x2 ¡ 4 ¡x l 3¡x 2x2 ¡ x ¡ 6 m x2 ¡ 3 x+1 n x2 + 1 x o x2 + 2x + 4 x+1 p ¡(x ¡ 3)2 (x2 + 2) x+3 q ¡x2 (x + 2) 5¡x r x2 + 4 (x ¡ 3)2 (x ¡ 1) s x¡5 +3 x+1 t x¡2 ¡4 x+3 u 3x + 2 x ¡ 3 ¡ x¡2 x+3 E INEQUALITIES (INEQUATIONS) 2x ¡ 1 x+3 6 are examples of inequalities.

1 2 1 4 2 = 12 = 12 = 12 = 12 8 4 2 1 So, assuming the pattern continues, consecutive terms have a common ratio of ) the sequence is geometric with u1 = 8 and r = 12 : ¡ ¢n¡1 ) un = 8 12 or un = 23 £ (2¡1 )n¡1 un = u1 rn¡1 = 23 £ 2¡n+1 1 11 u12 = 8 £ ( 2 ) = 23+(¡n+1) = 1 256 1 2 = 24¡n Example 7 k ¡ 1, 2k and 21 ¡ k are consecutive terms of a geometric sequence. Find k. CDR Wednesday, 24 October 2007 12:40:05 PM PETERDELL fr = 7g fr = 3g IB_HL-2ed SEQUENCES AND SERIES (Chapter 2) 61 Example 8 A geometric sequence has u2 = ¡6 and u5 = 162.

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