a) Use the Taylor theorem for function U(x, t) with the step size At. (x, isheld constant)b) Consider the second-order truncation error (0(At )²) for the Taylor formulaand then, obtain a finite difference approximation for the first-order derivativeof Urespect t ( U; (x, t)).

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Answered: a) Use the Taylor theorem for function…

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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3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax ) (t, is held cons. b) Consider the second-order truncation error (0(Ax )2) with the step size (-Ax) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)). c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then, subtract them and finally obtain a finite difference approximation for the first-order derivative of U respect x (Ux(x, t)). d) Consider the fourth-order truncation error (0 (Ax )4) with the step size Ax and also (-Ax ) then, add them and finally obtain a finite difference approximation for the second-order derivative of U respect x (Uxx(x, t)).
Rocky Mountain Chocolate Factory (RMCF) founder and president Frank Crail employs 220 people in 361 outlets in the United States, Canada, United Arab Emirates, Japan, and South Korea. If RMCF purchases 22.5 kilograms of premium dark chocolate at $16.80 per kilo, what is the net price with a 10/5 chain discount? Note: Do not round intermediate calculations. Round your answer to the nearest cent. Net price
Let f(x) = sinh x, where sinh x = ! 2 Find f"(x). Find the Taylor nolynomial of the function f(r) about Y= Infa + 2)
3) a) Use the Taylor theorem for function U(x, t) with the step size(−Ax ) (t, is held cons. b) Consider the second-order truncation error (0(Ax )²) with the step size (-Ax ) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)) . c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then, subtract them and finally obtain a finite difference approximation for the first-order derivative of U respect x (Ux(x, t)). d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then, add them and finally obtain a finite difference approximation for the second-order derivative of U respect x (Uxx (x, t)).
Consider the function f(x) = Vx + I. Compute f'(x) and f"(x). • (a) • (b) ) Write down the Taylor polynomials T1 and T2 of the function f at the point a = 0. • (c) DWhich value of b makes f(b) equal to V1.4? • (d) ) What are the estimates of V1.4 given by Tj and T2 from part (b)? (The actual value of V1.4 is about 1. 1832.)
a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider the second-order truncation error (O(Ax )²) with the step size (-Ax ) and then, obtain a finite difference approximation for the first-order derivative of U(x, 1) respect x ( Ux(x, t)).
Q2 Consider the function f: f(x, y) = x² - 4x + y² - 6y a) : ] Find all critical points of f. b). Find the maximum rate of change of f at the point (-1, 1) and the rate at which it occurs c) zero. Find the point at which the rate of change of f in the directions of i and j is

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a) Use the Taylor theorem for function U(x, t) with the step size At. (x, is held constant) b) Consider the second-order truncation error (0(At )²) for the Taylor formula and then, obtain a finite difference approximation for the first-order derivative of U respect t ( U;(x,t)).