3. Use the recurrence relation to obtain ex ,P(x),P,(z),B(x), assuming that P)(z) = i. Pi (x)-z. ...
(a) Use the generating function of the Legendre polynomials: G(u, z) = (i) to determine the oddness or evenness of the Legendre polynomial P) de- pending on n; (ii) to obtain the particular values P) and P-1); (iii) to show that and then to deduce (n + 1)P,n(x) = (2n + 1)2Pa(z) _ nP,-1(x), n-1,2,
(a) Use the generating function of the Legendre polynomials: G(u, z) = (i) to determine the oddness or evenness of the Legendre polynomial P) de-...
(3) Let m,n E N. Let p(x), i -1, ..., m, be polynomials with real coefficients in the variables -(x,..., rn). Prove that pi(r) p(a) Un (r)」 is a continuously differentiable map from R" to R". (Suggestion: Use Theorem 9.21.)
(3) Let m,n E N. Let p(x), i -1, ..., m, be polynomials with real coefficients in the variables -(x,..., rn). Prove that pi(r) p(a) Un (r)」 is a continuously differentiable map from R" to R". (Suggestion: Use Theorem 9.21.)
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
4.(10pts) Write Laplaces' equation in cylindricaol co-ordinates(p527 ex.3,use pinstead ofr) Assume the solution, e, φ, z), n can be written φ (p, φ, z)s u(p, φ)e-kz and Show that the equation for u is the two dimensional wave equation; Written in polar co-ordinates:xpcosp,y psinp For a plane wave traveling in a direction defined by:4-kcosce, ky-kinα Show that the plane wave solution can be written; look for a solution u z(x)en (2-n212,-0 And the equation for Z, is Bessels equation:Zh "x2...
Obtain a rough estimate of all real roots of the function f(x) = ex-x-2 by incremental searching in [-2,2]. Use Ax- 1. b) Obtain two iterating functions for finding each of these roots by fixed-point iteration by solving for each x which appears in the equation. c) Without doing any iterations, determine if each iterating function will converge to each root and ether the convergence or divergence will be monotonic or oscillatory [25] a) 1. d) From the iterati ng...
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
3. DO NOT USE CALCULATOR for this problem! Find the EXACT VALUES for all the parts. Given the function f(x,y) (a) Calculate the total differential of z at the point (x, y, z) (b) Use the total differential to estimate the value of f(1+2(10200),-1 3(10-200). [ Hint : dz= 2(10-200) dy=_3(10-200)]. (c) Calculate the exact diffe ( f(1.-) I Note: total differentiala exact difference. ] rence of f(1+2(10-200)10 200))- (d) Find an equation for the plane s-L(x,y) tangent t(:-: f(z,y)...
1. tain a rough estimate of all real roots of the function f(x) searching in [-2,2]. Use Ax1 ex-2 by incremental b) Obtain two iterating functions for finding each of these roots by fixed-point iteration by solving for each x which appears in the equation c) Without doing any iterations, determine if each iterating function will converge to each root and state whether the convergence or divergence will be monotonic or oscillatory d) From the iterating functions obtained in part...
Find the maximum and minimum values of the function g(0) interval [o. 7 2θ-4 sin(θ) on the Preview Minimum value-pi/3+2pi Maximum value O Preview Given the function f(z) = 2e - List the x-coordinates of the critical values (enter DNE if none) DNE List the x-coordinates of the inflection points (enter DNE if none) DNE List the intervals over which the function is increasing or decreasing (use DNE for any empty intervals) Increasing on DNE Preview Decreasing on -1/5 *Preview...