I need the answer as soon as possible How did heget the derivative?Ux =d (uxN, 2))dxthen2 (un)32x2(x*+y42y%I (x++y72y%Denotethem Fox =3x2itAnalogously,Fyy322thenFax + Fyy + F2z3(x7 4 2)-33we conclude thatFex + Fyy + F2z =0

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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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A- The goal of this part is to find an approximate value of In(1.1) by using the Taylor expansion. We consider the function f(t) = In(1+t). Show by induction on n that, the nth derivative of f is given by: %3D f() = (-1)~-1 (1n – 1)! (1+t)" Write the nh Taylor expansion of f at a=0 with the remainder R.. Show that max If(n+)(t)| = rn! tel0,0.1] 10-(n+1) when z = 0.1. Deduce that |R,S Deduce how many terms in Taylor expansion of f at a = 0 do we need to approximate f(0.1)= In(1.1) within 6 decimale places. The goal of this part is the calculation of limits of functions by using the Taylor expansion. By utilizing the MacLaurin-Young formula of order 2 of cos r and sin r determine the limits 1- lim n+1 Isin r Z-0 2-2COS z COS T 2- lim 240

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