Answered: sint+e 7,0 ≤ ≤ 1, y(0) = 0, hmar =…

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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1 Consider the roots (zeros) of f(x) =a³ – 4x + 1. 7+ 6- 5- 4- -4 -3 -2 3 -1- -2- -3 -4 -5+ We will see that small changes in the choice of x, produce different roots, or none at all. For each x, given, state the root (zero) of f(x) to which the algorithm converges, or write DNE if it does not converge. round to 3 decimal places If x, = 1.85, then Newton's Method converges to: x = If r. 1.7, then Newton's Method converges to: * = If To 1.55, then Newton's Method converges to: 2 = 3.
1. Draw the flowchart and trace table for the exponential function shown below. The Algorithm should request from the user the value of "x" and the number of iterations (approximation-stopping point). Both should be positive integers. For the factorial, you can use the built-in function, or in other words, you can represent the factorial (n!) as a Predefined Process 1=1+x+x²+x²³...
Solve the following nonlinear programming problem min c"r subject to a"Qx = d where Q = Q" > 0 and d > 0.
Use the linear finite difference algorithm to approximate the solution to the following problems.
Solve the following linear programs (LPs) using the simplex algorithm. • For each tableau you obtain, write the associated BFS and its objective value. • For each LP, find the complete optimal solution set and write it using appropriate mathematical notation. Use only the information in the tableaux to justify your answer. maximize z(x1, x2, x3) = subject to -2x1 + 4.x3 + 2.x3 0
which of the following is true
please can you do question 2 aswell. Thank you
4. Solve the following LP problem using the simplex algorithm for maximum tableaus: Maximize: f(x1, x2, 3) = 1 + 2x2 + 2x3 subject to ₁+ 2x2 + 2x3 ≤ -4 2x1 + 3x3 ≤ 5 2x1x2 + x3-4 X1, X2, X3 20
3 (a) Using Euclid's algorithm, solve the equation [25]57 X = [4]57 for X € Z57. Show your working. (b) Find all solutions to the equation [50]114 Y = [8]114 for Y Z114. Justify your answer. [Hint: for part (b) you should notice that ([50]114)-1 doesn't exist. Instead, write out what the equation means in terms of ordinary integers, and then relate it to part (a).]
4. Consider the following LP: max z = 6x1 + x2 X1 + x2 5 5 2x, + x2 < 6 st. X1,x2 2 0 (a) Solve this problem using the Simplex Algorithm and obtain the optimal tableau for this problem. (b) If we add a new variable x3 such that: max z = 6x1 + x2 + x3 X1 + x2 + ax3 S 5 2x, + x2 + bx356 X1, X2, X3 20 where a and b are scalar values, define the conditions under which the current basis stay st. optimal.
Please answer correctly. Write by hand please.

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sint+e 7,0 ≤ ≤ 1, y(0) = 0, hmar = 0.25, hmmins = 0.02, TOL =