PLEASE ANSWER ALL PARTS!! 1. (20 points) Define f(x) = x - 1 on [0,3]. Let g be the even extension of f to thewhole line (-0,00).(a) (4 points) Write out the formula of g on [−3,3].(b) (6 points) Sketch the graph of g on the interval [−9,9].(c) (10 points) Find a cosine series representation for f on [0,3].

(a) Find the formula for g(x)g(x)g(x) on [−3,3][-3,3][−3,3]Since g(x) is the even extension of f(x),…

Answered: 1. (20 points) Define f(x) = x - 1 on…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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13.) Find a power series for the function f(x) = = 5 2-6x3*
23.Determine the an so that the equation ∞∑n=1nanxn−1+2∞∑n=0anxn=0∑n=1∞nanxn−1+2∑n=0∞anxn=0 is satisfied. Try to identify the function represented by the series ∞∑n=0anxn∑n=0∞anxn.
Using basic real analysis 1, solve the question
It can be shown that the series 26•(-2)" ·x²" converges to f (x)= 6 on the interval 2n • X 1+2x? n=0 1 So, what does the series 127 1 (-2)" x²n-1 converge to? n=0 7.
3 (5) Let (r) = x? + 7x + 12. converges. A f(a) = *+3 B (b) Find A and B so that x + 4. As always, show all your work. Fine f(2) de (c) Find./1
Lemma 4. Let {yn} be a positive solution of equation (1.1) with the corresponding sequence {z„} e So for n > N. Then: (i) (1– p)zn N; (ii) {zn¢n} is increasing for all n > N. Proof. Assume that {yn} is a positive solution of equation (1.1) with the corres- ponding sequence {zn} E So. Then z, is positive, Zn 2 yn, and Yn = Zn – Pnyo(n) 2 (1– p)zn, n>N> no, so (i) is proved. It easy to see that z, E So implies lim b,(Az,)“ = 0; n00 otherwise we would eventually have Az, > 0 contradicting z, E So. Similarly, lim a„A(b,(Azn)“) = 0. A summation of equation (1.1) then yields 9szs+1 Zn+1 LIs. s=n s=n s=n Summing once more, we obtain as t=s s=n or Azn 2-Zn+1Qn. Hence, A(zn&n) = PnAzn + Zn+1Ao, > Zn+1(A0n – OnQn) =0 since {0,} is a solution of the difference equation (Ao, – Qnºn) = 0. Therefore, {z,9n} is increasing and this completes the proof of the lemma.
please help me with that
can you please write each step clearly and on paper
Use the power series X f(x) = (1-x)² Select one: a. c. x e. Ση·(-1)*·(x)" n = 1 x 1 1-X Ση·(x)+1 n = 1 En.(x)" n = 1 = d. Σn (-1)" (x)” +¹ n = 1 Σn. (x)n-1 n = 1 x Σx", x<1 to determine a power series for the function n=0
Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini

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1. (20 points) Define f(x) = x - 1 on [0,3]. Let g be the even extension of f to the whole line (-0,00). (a) (4 points) Write out the formula of g on [−3,3]. (b) (6 points) Sketch the graph of g on the interval [−9,9]. (c) (10 points) Find a cosine series representation for f on [0,3].