Let x_n be a Cauchy sequence in E. Also it is Cauchy in X as X complete so it converges at some point of X say a. Now as E closed so by definition a should be in E. Hence E is complete.
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a bonne n-m and cons ider e pime ectorhon e ho P fr (> Let p73 be a prime nmber and Consider as in ) Prove (a)よreach ief,,.., r an efemen
a bonne n-m and cons ider e pime ectorhon e ho P fr (> Let p73 be a prime nmber and Consider as in ) Prove (a)よreach ief,,.., r an efemen
an = −an−1 + 6an−2 , ∀n ∈ Z, n ≥ 2 , a0 = 1, a1 = 2 . (a) Write out the first 5 terms of the sequence. (b) Find the characteristic equation. (c) Factor the characteristic equation. (d) State the explicit formula for an. (e) Using the explicit formula found in part (d), write out the first 5 terms of the sequence. Verify that these terms are the same as part (a).
T25-1] 4 1and A0 1-1. Is u in the subset 4 14. Letu-1 0」 of R3 spanned by the columns of A? Why or why not?
Consider the polynomial P(n) of degree k: P(n) = aknk + ak-1nk-1+…..+ a1n + a0. with all ai > 0 Using the definition of Θ(nk), prove that P(n) € Θ(nk).
) Consider the following algorithm procedure polynomial (c, a0,a1, …, an) power :=1 y≔a0 for i=1 to n power≔power*c y≔y+ai*power return y Find a big-O estimate for the number of additions and multiplications used by this algorithm.
In Exercises 1–12 find the coefficients a0,. . . , aN for N at least 7 in the series solution y = SUM∞ n=0 anx n of the initial value problem. 1. (1 + 3x)y" + xy' + 2y = 0, y(0) = 2, y0 (0) = −3 7. (4 + x)y''+ (2 + x)y' + 2y = 0, y(0) = 2, y0 (0) = 5 Please help with both, thank you!
Horner: Given the coefficients of a polynomial a0, a1, . . . , an, and a real number x0, find P(x0), P′ (x0), P′′(x0), P(3)(x0), . . . , P(n) (x0) Sample input representing P(x) = 2 + 3x−x 2 + 2x 3 , x0 = 3.5: 3 2 3 -1 2 3.5 the first number is the degree of the polynomial (n), the coefficients are in order a0, a1, . . . , an, the last number is x0....
Sketch the following equations:I. X(n) = ??
(n) - ??
(n-3) – 4U II. X(n) = U(n)- U(n+4) + ∂ (n-3) III. X(n) = 2
?
[U(n)- U(n-6)]
ament 6-Chagter 7 Complete these S,2 reactions: 2n2 n 3 n4 n 5 2n 6 2n7 n 8 Get help answering Molecular Drawing questions (a) O +NatC +CHCONa Edit ethanl n11 n12 n12 n14 Get heip answering Molecular Drawing questions. b) on 16 n12 on 18 on 19h on 20 Na I Edit CHCHCHCH,+CH CH,S Na acesone an 21 Get help answering Molecular Drawing questions ults by Study (c) CH3 Na Br Edit CHCHCH CHBr NaI 4 acetone (d) по...