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)).

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)).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

See similar textbooks

Similar questions

Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii a1=0.1 11. Consider the function f(x)=4x2(1x) a. Find any equilibrium points where f(x)=x. b. Determine the derivative at each of the equilibrium points found in part a. c. What does the theorem on the Stability of Equilibrium points tell us about each of the equilibrium points found in part a? d. Find the next four iterations of the function for the following starting values. i. a1=0.4. ii. a2=0.7 e. Describe the behavior of successive iteration found in part d. f. Discuss how the behavior found in part d relates to the results from part c.
Assume x and y are functions of t. Evaluate dydtfor each of the following. 2xy5x+3y3=51; dxdt=6,x=3,y=2
A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
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 (O(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)).
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)).
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)).
c) Consider the third-order truncation error (O(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 )*) 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)).
(7) (a) Find the linear approximation L(x, y) to the function f(x, y) = √√r² + y² + 4 at the point (3,6). (b) Approximate the number (3.015)2+4+ (5.9919)2 using (a).
Let f(a, y) = 3x² + 4y2 – axy. (a) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive x-direction. (b) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive y-direction.
Let f(x) = 5x². a) Find the linearization L(x) off at a = 2. b) Use the linearization to approximate 5(2.1)². c) Find 5(2.1) using a calculator. d) What is the difference between the approximation and the actual value of 5(2.1)². a) The linear approximation is L(x) =