-kr i) Using the Cartesian position vector r, show that V (1) - ||r||*+2* ii) Consider some arbitrary function f(x, y). If the coordinates are rotated such that f takes the form f(u(x, y), v(x, y)) with u = x+my, v=mx-y, m € R, show that af (31) ()² + ( )* = (m² + 1) - ¹) (()* + (+)'). ду iii) Use the total differential or tangent plane or first order Taylor series to compute an approximate answer to f(3.8, 9.25, 15.9), given f(x, y, z)=√xyz and the expansion point (ro, yo, Zo) = (4, 9, 16).
-kr i) Using the Cartesian position vector r, show that V (1) - ||r||*+2* ii) Consider some arbitrary function f(x, y). If the coordinates are rotated such that f takes the form f(u(x, y), v(x, y)) with u = x+my, v=mx-y, m € R, show that af (31) ()² + ( )* = (m² + 1) - ¹) (()* + (+)'). ду iii) Use the total differential or tangent plane or first order Taylor series to compute an approximate answer to f(3.8, 9.25, 15.9), given f(x, y, z)=√xyz and the expansion point (ro, yo, Zo) = (4, 9, 16).
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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Transcribed Image Text:-kr
i) Using the Cartesian position vector r, show that V
||||*+2
ii) Consider some arbitrary function f(x, y). If the coordinates are rotated such that
f takes the form f(u(x, y), v(x, y)) with u = x+my, v= mx-y, m R, show
that
2
2
2
af
()*+()*
= (m²+1)
(()*+())
Əv
iii) Use the total differential or tangent plane or first order Taylor series to compute
an approximate answer to f(3.8, 9.25, 15.9), given f(x, y, z)=√xyz and the
expansion point (xo, yo, 20) = (4, 9, 16).
Continued..
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