ANSWERS TO EXAMPLES
CHAPTER III
- x=12 or -16.
2. nth term =n2+n—3+3". Sum of n terms =2n3+6n614n—9+32 1 zo3. 51224.4.2 .22!•(3x+1)(3x6x + 209+4) ..(3x+70)' 5. 3". 2a !.6. 2"'-2 (m+1) (m+4).CHAPTER IV1. f(3)=75857'2; f(4)=776238; f(5)=79432.0.2. 02017.3. 69215.4. 12, 14 ; 26, 42 ; 138, 266.5. 97357.6. 97453.
- 0 f (0) _ -1.753875, A2f(0)= —'07725 and A3f (0)=.00125 from which
the series may be completed.
- '1954.
4f (1)=1.1006, A2f(1)='1083 and A3f(1)=•0137 from which the values off (x) required may be found.f(5)=3211; f(6)=661.x4— 2x3 + 3x2 — 4x + 5 or 24.2x—8x2—18x—19.
- log 45 =1.65321,log 46 =166276,log 47 =1.67210,
log 48 =1.68125,log 49 =1.69020.
- 58843M.
CHAPTER V1. 2290.0.2. 5. The series is f (25)f (29)f (33)
| 95384. |
|
3. |
•3165. |
4.01625. |
| 568, |
f (26) |
585, |
f (27) 602, |
f (28) |
6•-21, |
| 644, |
f (30) |
671, |
f(31) 707, |
.f (32) |
747, |
| 793, |
f (34) |
843, |
f (35) 897. |
|
|
1.
CHAPTER VI
1. 2.731. 2. 2 * . 3. 16.9. 4. 37.2. CHAPTER VII
1 1 11
1—r n(n+1)(n+2)...(n+r—2)' 144' 4. '0525.
CHAPTER VIII
1. 6895. 2. 460. 3. •500.
ANSWERS TO EXAMPLES 151 CHAPTER IX
1. (i) 10.389; (ii) 10.475. 2. 3.297. CHAPTER XI
- 1-10• -x4+6.x2+4x-21
x2(1g x)e (x—1)2(x2—3)i(x2—7)Ix2 (3a2+2a.v+x2)1
- 3 (a+x) (a2+x2) (a2+ax+i2)3. x3 A/ -2
4. (1) az xxloga.logu+axlog'5 a Toga+1)+1 ,
(:)ax/ (2)- 1(3) 3x(log x)2(log x)2x 9-1 'x5 -y(1-x)v-1-(1-y)xlog(1-?1)6. 1 tog a , exxxx(log x+1).x(1-y)x-1_(1-x)vlog(1-a)'xCHAPTER XII
- (1 (-1)n.n!r1-12(n+1)2 xlogae
4L(x-1')n+1 (x+l)n+t (x+l)n+2j' () (1+x.)3.
- ea,. .an-2 [a2 (x-2)2+2na(x-2)+It(n-1)].
4. 2 [ab + x (6ca - b2) - bc.v2 - 2c2x3] (a+bx+cx'j25. (-1)n. n! (2x5-.2n + - (2 x--1)n+1CHAPTER XIII
- tox - x3 + 3x5+(-1)r 1.3...(2r-l)x2r+1
g a + a 6a3 40a°rl (2r+1)2ra r+1
x2 5x3 x4 209x°
- x-2 12+4+ 20
CHAPTER XIV1. 1.2. 3~3.3. ±2 .4.157 miles from the nearest point5. f(2)=218, f(4)=0, f(5)=-19.Maximum value when x=120+11110 30Minimum value when x=120 -1/110 306. Minimum values- 3, - 128. Maximum value 0.7. 2 (7r12m+4)8. (1) N/- . ar"-n; (2) 1.
152 ANSWERS TO EXAMPLES
CHAPTER XV
3. — •06353.
CHAPTER XVIII
/ 3
1. (1) 2 35 1 (5x3+6x2+8x+16)+c; (2) S- log (~,3+a3)+c;
(3) log x [log (log x) -1] +c. \
r x4 4x3 12x2 – 24x 24
2. ax [l,g a
e (log,a)2 + (log,a)3 (log,a)4 + (1og,a)51+C.
3. (1) -i [(x+a)%/z2+2ax—a2log{(x+a)+Vx3+2ax}+c]; (2) k(a2—x2)1—a2'/a'—x2+c; (3) llo xx+log (1–x) +c. 4 2(x–3)2+2logx+4+c.
6
a
5. log x–1 +x11+c; (1+x)log(1+x)–(1–x)log(1–x)–2x+c;
x,t+1
(n+1)4 [{(n+1) logx}3—3 {(n+1)logx}2+6 (n+1) logx—6]+c.
CHAPTER XIX
1. [3.f(0)+6.f(1)—f(2)]; [—3.f(0)+4.f(1)—f(2)]; [5.f(0)+8f (1)—f (2)1
2. :311 . 3. 1og,6. 4. . 5. CHAPTER XX
1. 262112. 2. 32500. 3. (1) –lac; c. (2) -16.5; 33.5.
4. i [3f (– 2) +2 f (0)+3 f (2)]. 5. 20.4 miles. 6. 14262.
CHAPTER XXI
2. (1) -11a; (2) N ;. 3. 7s. 4d., 7s. 4d., 7s. 4d. 4. 0000179.
5. (1) *; (2) 6. gs q. 8. 171b6•
9. . 10. 31466. 11. 30:31. 12. H.
13. 2109. 14. (1) s ; (2) A; (3) . 15.
16.. (1) g ; (2) 1g$a. 17. A's chance i U e s ; B's chance 1 jOy y13.
18. •01111. 19. 8 log 2 – 3 20 101,232
64 log 2 – 15' 609,966,275 '
21. al. 22. —ilog3.
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