319
ANSWERS
2 (a) (c)
l-4x+16x 2 (b) 1+6x+24x 2 1+12x+90x 2 (d) 1-x+%x 2
3 (a)
84
(e)
~
(h)
i n(n + l)(n + 2)c
4 (a)
(b) -8
-20a
(f)
l+jx-~x
6 (a) (e) (h)
7 (a) (c)
-i
(g) 20b
(d) 256
3
3
(b) 1+%x-~x
2
2
(d) l+ix+~x
2
11
(c)
i.r
(d)
3 20 (f) ~..J2 (g) -ft,-a 3 fgn(n+2)(n+4)b 2 4 1-ix-Js-x (b) l+ix 2 -Js-x 2 2 2+{x-okx (d) 6+%x-'4-x
-i
8 lxl<j (a) 4+12x+27x 2 +54x 3 2 3 (b) {+%x+ftx +짜x 2 3 9 (a) 1-3x-ix -짜x ,lxl<f; 2 (b) 1-5x+25x -125x 3 ,lxl<! (c) (d) (e)
(f) (g) (h)
(i) (j) (k)
2
1-3x+18x -126x 3 ,lxl<~
1+8x+40x 2 +160x 3 ,lxl<i 4 4 2 l+x -ix +ix ,lxl<i..'2 2 2-jx-~x -~x 3 ,lxl < i 2 10-4x+~x -~x 3 ,!xi< 5 2 3 l+ix+{x +ix ,lxl<2 2 i-~x+~x -:frx 3 ,!xi< 2 2x-Ix4+3x74 b4 m5 xlO , lxl<V4 2 3 1+2x-6x +28x ,lxl<i 2
3
j-!짜-..J3x + ~x + ~..J3x , Ix I< ..J3 10 1+4x-8x 2 +32x 3 ,1.039 232 (a) 10.392 32 (b) 1.732 05 2 (a) 5.06578 (b) 9.99667 11 l+jx-!짜-x (I)
12
2
l+{x-~x
6
15 2 1+3x+Jfx , lxl<{, 4.123 15 4,6,-100 4 16 l+x+2x 2 +3x 3 +5x ,l.001002003005 13
17 (a) 2-2x+ix 2
(b) 1+5x+6x
2
-~
i-%x+3x
13
n=l5, 1-ix-ix
2
1 1+5x+Jfx +ix
3
2 1-2x-2x 2 -4x 3 3 1-6x+24x 2 -80x 3 4 1-4x2 +12x 4 -32x 6 2 5 2+{x-okx ,!xi< 4
2
,
-WJ
lxl<{ 16 (a) 1-2x+3x 2 -4x 3 4 6 2 (b) 1+2x + 3x +4x 4 6 (c) 1-4x 2 +12x -32x 15
17 A=l,B=-1,C=O,D=l,E=-1 (a) 0.999 700 000 026 9919 18 1+2x + 3x 2 + 4x 3 , 1.000 200 030 004 2 19 1-{x + :frx , 1.495 35 20
1-ix+~x 2 +ft;x 3
23
l+ix+~x , 3.605 525 2
24 1-2x+4x 2 -8x 3 +16x 4 , 0.346056,0.69 2
3i4
3+ix+ix , 26 1-2x 2 +15x 4 , 0.531
25
15 Rational functions Exercise ISA (page 201) 1 (a) 2x-4 (b) 3x+2 (c)
x 2 -3x+6
(e)
(x + 3)(x- 2)
2 (a) 5
3 (a) (d)
4 (a) (d)
Miscellaneous exercise 14 (page 195)
2
2
12
(d)
14
18
2
7 l+ix-ix ,a=2,b=-% 8 1+2x + 3x 2 + 4x 3 , a= 5, b = 7
4+x-Jkx ,lxl<~ 2 3 10 1-jx-~x -fix
(b) 1-x+2x 2 2 (d) l+ix+ti&-x
W
(b)
4 2 _ 3x +15x 4 2 2a 8a
9
2
1-ix+~x 5 (a) 1+2x-2x 2 2 (c) 1-8x+8x (c)
(c) -270 3
6 1
5 (a) (c)
(e)
-1
x+4 x+6 x-3 5x 12 x- 7 15
8+3x 4x 7 12x
(d) _1_
3x+2 1 (f)
x2+x+1
(b) l 4 (e) 1
(c) (f) 1
(b)
(c) 3x+2
(e) x+4
(f)
3
. x+7
x-4
2x+l -2(4x+5) 3x+l
(c) 7x+ll
(b) 25x
12
12 (f)
4 (b)
13x+14 5
2
2x
(d) 3x-5 (f)
2x 2 x +2x+l x2