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- Find the series representation: s1=1/3^0 s2=1+1/3^1=4/3 s3=1+1/3+1/9=13/9 s4=1+1/3+1/9+1/27=40/27 s5=.....+1/81=121/81 s6=.........+1/243=364/243find fourier series on [-T, T] fex)=IsinxlTaylor's series expansion of simox) is given by Sincx) = X- ++ (assumed as exact function) 31 By constdering with two terms Sincx) = x-, compute the true percent relative errors Et6 for X=T/6 0.50 1.35 0.20 0.35
- ® find Fourier Seoies Series 1, 027くt f(x)%=D} <り< 2.Determine the Taylor Series of e^(2x) at x=1. (A e? (x)" n! n=0 (B e? (2x) n! n=0 e? (x)** 2n! 00 (2æ)" (2n)! (D e2QID100624471041287 Which of the following is the left hand sum with n3D3 rectangles for f(x) = e" on the interval [-2,4]? 2(e° + e? +e*) 3(e? + e') 2(e 2 + e° + e2) e° + e2 + e4 3(e' +e*)
- 6 ) nt series. %3D im fen-(2-) im incll-2 (4) at n:326.0 VO KB/S LTED (0) 14 46, 4:27 f Assignment. o Sequence and Series 1. Find the limit of the sequence if it exists: 1-R (a) dn - 70 - 4n 70 - 4n2 (b) aa- (0.9)" (c) a, - (10n) /n (dja, = (e) a, = » (1- cos-) (C da = tanhn 2. The first term of the sequence is z, = cos(1). The next terms are zy = 21 or cos(2), whichever is larger; and = g or cas(3), whichever is larger. in general. at1= max{r, COs(n +1)} Check the convergence or divergence of the sequence. (2n + 3)! (n + 1)! 3. Check the convergence of the soquence an = 4. Find the sum of the following series: (a) Ei-1 4" 2+1 (b) E 5" 1 (e) E 21/n+1) 5. Check the convergence of the following series: In (b) n 6. Check the convergence of the following series: (a) (1-)" Stan-' (b) 1-n? 1/n (c) TInnyn" n - 1 7. Show that n(ln n) if and only if p >1. 8. Which of the series converge, and which diverge?: (a) (b) Esin ! 1 (c) E 1+ In' n (d) (In nja (e) E-) n! Inn (C 2 in + 2) n(n + 2)! (R) (h) (n") * 1.3.5.(2n - 1) (1) -2.4. (2n) (3" + 1) 9.…5. Using the Taylor series of e^x about x = 3, find the first three terms of Taylor series andthe error in terms of h for e^(3−2h)..