Question

5. 192 + ... complete the following statements using 125 For the G.P. 3 + 2 + 2 + rational numbers. i. a = ii. r= [1] [2] [2] iii. S. = b) Complete the following statements. i. 1- x + x2 – x3 + x4 - ii. In(1 + x) = —... = [3] [3] Page 3 of 4

Answer 1

Given GR. 3+12 + LS 25 + 192 125 커 5 i Weknow a=3 1 Ciscommon ratio o= 에에에 (2 5 3 ) 현물살 = 12 5 8 - 5 a Cit) so A-8 W 또 어 3 (50 5 - 3. ( = 3x5 = IS Soo = IS

AWWF ci) a=3 8- =놓 (iii) Soo=15 (이 2 2324 1+ 지 1) CD1-L-1) 2+ DADA-23 커 2) ! + is in the form of = (+ 끼n-2, 끼n-) (M-2) 정 끄t + In-) t 3 커 킹 그세 X=X Wehave binomial expansion of (142M = H = (++mn- 2 의 , 구 3] 1 + px + LIC D-DC-223 2 (+)) Answer i 나즈 2424 = (+)

cii) en tx) maclarin's series expansion function f(x) = f(0)+xfx0) + a F"(0)+*<"60)+-- wehave f(x) = ln (Ha) f(0) = incito) I ln (1) f(0)=0 differentiate 0 on both sides f(x)= (ancta) de f'(x) = 42 2 sco)= 1 to f(0)=1 differentiate on both sides f (x) f" (0) da(ita) (142)2 3 f'(o)= tez (140)2 f'(o)=41

differentiate on both sides f(x) elle (1+x)? (1+x) -6-20170524) f"CX) 2 (1403 f (o)= 2 (to)} f (o)=2 20 23 111 .::f(x) = f(0) +5fCo+ f (0)+ (o)t2 CO)+-- 2! e3 f(x) = 0+2011+ 2? (0+ (2)+ 3XXXI 2X1 f(x) = 2-2 + le) Answeri 22 en(1+x)=x- + 23