1. Find the output y[n] of the DE y[n] = 2x[n] + 3x[n-1] - x[n - 2] in the simplest form for each of the following cases, assuming zero initial conditions: i. x[n] = 2, n ≥ 0 ii. x[n] = 5n, n≥ 0 iii. x[n] = =4 (9)". n≥0 iv. x[n] = 10 cos(nл/2), n≥ 0

Suppose that a new company begins its operations in 2020 and the size of the company over the next 10 years is predicted by N ( t ) = t3 − 12t2 + 45 t + 5,   0 ≤ t ≤ 10 where N is the number of employees t years past 2020.   In what year the number of employees will be the highest?

11.2.3 (a) Derive Eq. (11.35) (1 − x²)P(x) = (n+1)xPn(x) − (n + 1)Pn+1(x). (b) Write out the relation of Eq. (11.35) to preceding equations in sym- bolic form analogous to the symbolic forms for Eqs. (11.31)-(11.34).

1. Consider the function: x3 − 6x2 +11x − 6. This function has three roots at x* = 1, 2, 3. Q.At which points, the iteration methods fails (if any)? a. 0, 2+(1)/(sqrt(3)) b. 0, 2-(1)/(sqrt(3)) c. 0, 2+-(1)/(sqrt(3)) d. The method has no failing point

Suppose that the inventory of a certain item t months after the first of the year is given approximately by I(t) = 10 + 36t - 3t2, 0 ≤ t ≤ 12 What is the average inventory for the last quarter of the year? Answer: The average is                items

Solve b

30(2t et + 5) et The number of members of a newly founded club is given by M(t) members per month, where t is the number of months after its opening in the beginning of 2010, and t = 0 corresponds to January 1. What was the average number of members during the period comprised of February and March that year? [You should assume that all months have equal duration for the purposes of this problem.] Approximate your answer to the nearest integer. =

Find..

3. let A = [56] 58 Find +A e and Use it to solve x = Ax² AX with the Initial Condition x (0) = [2]

Compute y = F 8c by the three FFT steps for c = (1, 0, 1, 0, 1, 0, 1, 0). Repeat the computation for c = (0, 1, 0, 1, 0, 1, 0, 1).