4. Consider an underlying function f(x) and nodes at the locatons of oo+ h, for some ћ 〉 0, Assuming ћ is small enough so that f"(x) f"(y), for any x,y E f"(t) zo - h, + h], use the resu...
(3) Consider the expressions (a) Write down the Runge-Kutta method for the numerical solution to a differential equation Oy (b) Show that if f is independent of y, i.e. f(x, y) g(x) for some g, then the Runge-Kutta method on the interval n n + h] becomes Simpson's Rule for the numerical approximation of the integral g(x) dr. In this case, what is the global error, in terms of O(hk) for some k>0? (3) Consider the expressions (a) Write down...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn (a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...
1. Let ab and f E C[a, b], and let E(0, ))- - (co +c)w(a) da for some weight function w(x) >0. (a) Use calculus to write down a linear system for the critical point of E(co, c1). (b) Is the solution of this linear system the same as that of the normal equations arising from the use of Theorem 2 on page 395 to optimize co, ci under the norm 1/2 ? (c) Use your results to find the...
e) y_3cos(x +4) +4 MaxMinAmp riod f y 5 cos 2n(x -0.5)+5 V.T Max Amp Min AC SİNE function has a maximu m value of 4, aminimum value of 2, a phase shift of 1 rad to the right, and a period of 4. Write an equation for the function and graph the function [KU, 6m] 2. Min _Armp period. P.S V.T. . Equation 3. Determine the equation for the following a) COSINE function Equation b) SINE function Equation 4....