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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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If fufe. P:IR,i-ls---sn prove fnave diffa Veutable at XoeI thad 2) Cfisfn- Pu)isclifferantiable at %. ancde + fi (xo)f. (xo) - falxo)+--- +Pi(x) --
Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w = v? fuu + u? frv - 2uvfuv - ufu - vfy !3! dx2
The function fa)= 2 Vx-3'+6 is not one-to-ane. O True False
Dnd Zi if Zi=r [core tisin@] and
4.Plee the groph of fra) If prad (4) ond f")=lcg
integralf(x)dx z be[f(a) + f(b). Let h = b-a The trapezoid rule for estimate an a)Derive the error for composite trapezoid rule b) Determine the minimum number of the subintervals needed to approximate (x+edr to an accuracy of at least 0.5 x 10-7 using the composite trapezoid rule
3. If A² = [45] find A where A is upper triangulax
In 군 + x find the given equation det ermain z as adifferential X amd y function of
prove that if f(x)is derivable at a point say "a" then it is continous at x=a
Determine the interrah Con vergence for Hhe Toyber Saries polguamich in (1) (2x. 4? Al [t.o], Bl [-1,0],c)(-1,) g) (,o) h [0,2] 1 (-1)
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Show orthogonality of the functions on the interval cos(Lx), cos(2Lx), cos(3Lx), ... -T/L≤ x ≤ π/L and determine the corresponding orthonormal set of functions.

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on Give an crample of a dis continous bijection fo[at] = [1,2]