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).
Recursive definition for factorial: a0 = 1, an = n * an-1 procedure factorial(n: nonnegative integer) if n = 0 then return 1 else return n * factorial( n - 1 ) Trace the execution of the factorial algorithm described above for input 7. Track the number of times factorial is invoked (with the first invocation with input 7 as invocation 0) and the value returned by each invocation.
) 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....
1. Find convolved output of x[n]=u[n]-u[n-5] and y[n]=0.2^n u[n] 2. Find convolved output of x[n]=u[n-2] and y[n]=0.4^n u[n] Please use the DT convolution formula and show step by step!