Question

Consider the integral 1 To vita dx V1 + x3 (a) Write out the first four non-zero terms of the MacLaurin series for the above integral. (b) Write out the first four non-zero terms of the series for 1 so dx V1 + x3 (c) How many terms of the above series should we add together to estimate p1/2 dc V1 + x3 within 0.001? 1

Answer 1

(④) dn 21c 3 3 널 dx (( + 3 + 3 3~5 기 ( I*()* = { 1 - 글 ~ + 증 9 S x 16 yax 1 8 10 M 4 C 지 그 3 56 + ) 0 32 7 10 1 4. ~ + 3N Amwer Tita 55. 32. 1 da b) (12 J1+x) LA {1-xt 중이 37 Sn9 16 지2 + 3N 10 CL 32 1 + U 51 7 1 3월 128 7168 Ams 1 1 + 3. 2 128 7168 CScanned With CamScanner L 32768 ( i. รวาด 32762

< 0.001 (c we know I Rol=15-snls butl 3 ( 12 (1+x² +12 has (neiston term has follas 1"*E, ** nomai) (0+2) -- (n =) x dal (n+1)! 3n buti nad <0.001 z I /tinti n Inti) In+2) --In-1) 3n+11')2 (n+1)! 3nti < 0.00 1 1 <0.001 (2) 3nt 1 hintal (nt 2) --(n-1) (n+1)! (39+1) Put n=27, this inequality in satin fied So we have to add extra 2 3 more terms to get CScanned wit Estimate with in 0.001.
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