650 Solutions to exercises
34.Q 1 = 15 y
1
2
1 + 13 y
2
2
1 + 13 y
3
2
1 + 1 y
4
2
,
Section 19.5
39.(i)3 (ii)13 (iii)2 1 + 13 i
(iv)2 1 − 13 i
- in Ex. 37, in Ex. 38
Chapter 20
Section 20.2
- (i) (a)1.213 (b)1.213
(ii) (a)72.030 (b)72.03
(iii)(a)0.130 (b)0.1299
(iv) (a)0.002 (b)0.002499
- (i) (a)0.0005 (b)0.0005
(ii) (a)0.0005 (b)0.005
(iii)(a)0.0005 (b)0.00005
(iv) (a)0.0005 (b)0.0000005
- (i)6.289 1 ± 1 0.001 (ii)1.617 1 ± 1 0.0015
(iii)42.87 1 ± 1 0.015 (iv)10.11 1 ± 1 0.015
- (i) (a)0.0004 (b)0.0004
(ii) (a)0.000007 (b)0.00007
(iii)(a)0.004 (b)0.00004
(iv) (a)0.3 (b)0.0002
- (i)58.793 1 ± 1 0.243 (ii)8.764 1 ± 1 0.036
(iii)0.3540 1 ± 1 0.0008
- (i)(a)x
1
1 = 1 60.0,x
2
1 = 1 0.015
(b)x
1
1 = 1 59.9835,x
2
1 = 1 0.01665
(ii)(a)x
1
1 = 1 60.0,x
2
1 = 1 0.01667
(b)x
1
1 = 1 59.9835,x
2
1 = 1 0.0166713
00
0
00
−
−
i
ii
i
2
1
i
−i
00
0
00
00
0
00
i
ii
i
i
ii
i
−
−
−
−
,
2
1
2
1
−
−
i
i
i
i
,
1
3
21
2
− 3
−
−
−
i
i
i
i
i
i
i
i
,
y
y
y
y
xxxx
xx
1
2
3
4
1234
12
1
2
=
+++
+−−−
−−+
−+−
xx
xxxx
xxxx
34
1234
1234
- (i)0.414213562;4.9875621;49.9987;
500 ; 4900
(ii)0.414213562;4.98756211;49.9987501;
499.999875;4999.99999
- (i)0.175201194;1.66585 1 × 110
− 5
;
51 × 110
− 8
; 0
(ii)
(iii)1.666675000 1 × 110
− 5
;
1.666666668 1 × 110
− 9
;
1.666666667 1 × 110
− 13
Section 20.3
9.1.564 10.0.5314 11.1.322
12.1.5644623 13.0.53139086
14.1.3221854
Section 20.4
16.0.03973;0.25590;0.47703;0.72357
17.0.04037 (from x
0
,x
1
,x
2
);
0.25673 (from x
0
,x
1
,x
2
);
0.72425 (from x
3
,x
4
,x
5
)
18.0.257081 (from x
0
to x
5
)
Section 20.5
19.n 1 = 1 8: 0.95834 1 − 1 0.00284 1 = 1 0.95550;
n 1 = 1 16: 0.95622 1 − 1 0.00071 1 = 1 0.95551
20.n 1 = 1 4: 0.955559;n 1 = 1 8: 0.9555146
- (ii)0.9555117
22.0.94608
23.0.88208
- (i)0.095166
25.1.64493
n (i)n 1 ln 1 n 1 − 1 n (ii)‘accurate’ (iii)ln 1 n!
1 − 1 0.0003 0
2 −0.6137 0.693151 0.693147
3 0.2958 1.7917597 1.7917595
Section 20.7
27.x
1
1 = 12 ,x
2
1 = 11
28.x
1
1 = 11 ,x
2
1 = 12 ,x
3
1 = 1 − 2
29.x 1 = 1 − 1 ,y 1 = 18 ,z 1 = 1 − 5
30.w 1 = 1 x 1 = 1 y 1 = 11 ,z 1 = 1 − 1
xxx
224
6
1
20 840
++