468 



PRACTICAL MATHEMATICS 



VII (pages 112, 113, 114) 



(10) e*(x + 1), e?(x + 2), &(x + 3), e*(x + n) 



(11) sin na-nx-- rsr + ^-z- ---.+ ... 



COS 



= 1 



"F 



(13) 

 (14) 



tan n ~ x x + tan n x+ n tan n+1 x), e* (1 + tan x + tan 2 x) 

 + 3 tan # + 2 tan 2 x + 2 tan 3 x) 

 e*(5 + 7 tan x + 11 tan 2 x + 6 tan 3 x + 6 tan 4 #) 



29 tan #+36 tan 2 #+52 Jan 3 #+ 24 tan 4 #+24 tan 5 #) 

 + 101 tan x+ 221 tan 2 # + 220 tan 3 x + 300 tan 4 x 

 f 120 tan 5 # + 120 tan 6 #) 



41# 5 



. 4- ,7?* -4- 



6 

 1 



tan # = x + x 2 + ~ 



120 

 (19) 4-4936 



a(l - cos 6) 2 

 (22) 3-424 (23) 



(24) # # 2 + # 3 # 4 + # 5 # 6 + 



(25) 1 - 



(20) 0-765 (21) 1-172 



VIII (pages 127, 128, 129) 



(!) 2/max = 35 ^hen a? = 1, /min = 26 when x = 2 



(2) ?/ m ax = 124 when a? = -5,y aan = - 76 when # = 5 



( 3 ) ?/nun = 80 when x = - 2, t/^ = 87 when x*= - 1, 



when # = 2 



= 48 



(4) 



= 7-213 when x = 0-8236 



(5) # = 1-877, t = 0-4163 

 (7) 



(9) 



(11) #=!,* = 0-3465 

 (13) # = 4-5, = 0-1439 



= 3-877, t = 0-2019 

 x = 5, i = 



(6) # = 3, t = 



(8) # = 1-840, * = 0-5 



(10) x - 6-065, * = 0-25 



(12) a; = 4, * = 



(14) 



= 1-345 when x = 3 



(15) rad. = 8-166", ht. = 11-54" (16) rad. = 7-07", ht. = 14-14" 



(17) rad. = 8-507 ", ht. = 10-51 " 



(18) rad. = 9-588 yds., ht. = 13-56 yds. 



(19) 2W = - 231 when # = 0-5777 



(20) 17-01 knots, 2488, 2460, 2483 (21) 15-7 knots 



