Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 78, Problem 14A
To determine
(a)
The sketch a rectangular solid formed by the angular surface edges.
To determine
(b)
The value of angle
To determine
(c)
The value of angle
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b please
(b) Let I[y] be a functional of y(x) defined by
[[y] = √(x²y' + 2xyy' + 2xy + y²) dr,
subject to boundary conditions
y(0) = 0,
y(1) = 1.
State the Euler-Lagrange equation for finding extreme values of I [y] for this prob-
lem. Explain why the function y(x) = x is an extremal, and for this function,
show that I = 2. Without doing further calculations, give the values of I for the
functions y(x) = x² and y(x) = x³.
Please use mathematical induction to prove this
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