Xo - ? Consider the following sequence: 0.2 1.3 4.4 X1 2 9.5 X2 - Xz...
Question 11 Consider the following sequence: 0-2 1.3 4.4 2 X2= 3 Хо- X1 - 13 X3 9.5 4 ... Calculate the general formula of this sequence. What is the value of X4? • do not write unevaluated expressions (don't use 12/4+1, use 4) • do not leave fractions, write decimal points (don't use 1/2, use 0.5) do not use Turkish a,bcd notation (do not use 1,234 use 1.234)
Consider the following sequence: 2.1 Xo = 0, X1 = 2 , X2= FC 2 4 Calculate the general formula of this sequence. What is the value of X 4? • do not write unevaluated expressions (don't use 12/4+1, use 4) • do not leave fractions, write decimal points (don't use 1/2, use 0.5) do not use Turkish a,bcd notation (do not use 1,234 use 1.234)
Question 1 [10 points] Suppose that the sequence xo, X1, X2... is defined by xo = 2, x1 = 1, and Xk+2 = Xk+1+2xk for k>0. Find a general formula for xk. Be sure to include parentheses where necessary, e.g. to distinguish 1/(2k) from 1/2k. . xk = 0 Official Time: 22:32:44 SUBMIT AND MARK SAVE AND CLOSE
We work with a sequence with a recursive formula is as follows, Xo = x1 = x2 = 1; In = In-2 + In-3, n > 3. The sequence therefore looks like: 1,1,1, 2, 2, 3, 4, 5, 7, 9, 12,... For example, x3 = x1 + x0 = 1+1 = 2, 24 = x2 + x1 = 2, and x5 = x3 + x2 = 3, X6 = x4 + x3 = 4, 27 = X5 + x4 =...
Consider the ODE f(x,y) = - 10r5 Take initial conditions xo = 0 , yo = y(0) = 11 , x1 = 0.2 and y y(0.2)= 22, solve for y(99) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to approximate the next y solution. The general formula is: 3 Vi+2 i+1+ h 1 (owsan-cuea An example of the first few iterations is shown below. (wcomnce) (ceny5-cesn) y2 yh 3 (esa-c)...
Let a sequence Xo, X1,X2,... be defined in the following way: X12 1) Compute the first 10 terms of this sequence. (2 points) 2) Prove that this sequence is strictly increasing, .e., Vn 20:X >X. (2 points) 3) Prove that Vn 20: Xn S4". What are the base cases? What is the inductive step? (5 points) 4) The above result suggests that this sequence grows in the worst case exponentially, i.e., X 0(4). Consider trying to tighten this bound in...
2) 17pt) Solve the following IVP. Xi' = -X1 + (3/2)x2 x1(2) = 1 xz' = (-1/6)x1 - 2x2 X2(2) = 0
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| | xo = 0 Xi = 2 x2 = 4 f(x) = 2 f(x1) = 6 f(x2) – 10 Consider the differential equation dy – Ax+ 4 where A is a constant. dx Let y = f(x) be the particular solution to the differential equation with the initial condition f(0) = 2. Euler's method, starting at x = 0) with a step size of 2, is used to approximate f(4). Steps from this approximation are shown in the...
2. Now consider u(x1, x2) = 2 In xỉ + In xz (a) Find expressions for MUị and MU2. (b) Find an expression for MRS12. (c) Are the preferences represented by this function convex? Justify your answer using the MRS or a graph of some indifference curves.
Question 11 Consider the following sequence: 0 3 8 X2 6' X3 X 4 = 15 8 1... Calculate the general formula of this sequence. What is the value of X5? do not write unevaluated expressions (don't use 12/4+1, use 4) • do not leave fractions, write decimal points (don't use 1/2, use 0.5) • do not use Turkish a,bcd notation (do not use 1,234 use 1.234)