Let W be the plane with equation x + 2y +2z = 1. Define the function f (x, y, z) to be f(r, y, z) = distance from (x, y, z) to W. (a) For each real number k > 0, the level surface f(x, y, z) = k can be described in terms of other familiar surfaces. Give a geometric description of the level surface f (x,y, z) = k. Be as precise as possible when explaining your answer. %3D %3D (b) For each real number k > 0, produce an explicit equation for the level surface f(x, y, z) = k. (c) Consider the function g = f² (distance square). Find the partial derivatives (x, y, z) and Əzðy notice? dyöz (I, Y, z). What do you
Let W be the plane with equation x + 2y +2z = 1. Define the function f (x, y, z) to be f(r, y, z) = distance from (x, y, z) to W. (a) For each real number k > 0, the level surface f(x, y, z) = k can be described in terms of other familiar surfaces. Give a geometric description of the level surface f (x,y, z) = k. Be as precise as possible when explaining your answer. %3D %3D (b) For each real number k > 0, produce an explicit equation for the level surface f(x, y, z) = k. (c) Consider the function g = f² (distance square). Find the partial derivatives (x, y, z) and Əzðy notice? dyöz (I, Y, z). What do you
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:AM (2) - Edited
Let W be the plane with equation x + 2y + 2z = 1. Define the function f (x,y, z) to be
f(x, y, z) = distance from (x, y, z) to W.
%3D
(a) For each real number k > 0, the level surface f(x, Y, z) = k can be described in terms of
other familiar surfaces. Give a geometric description of the level surface f(x, y, z) = k. Be
as precise as possible when explaining your answer.
%3D
(b) For each real number k > 0, produce an explicit equation for the level surface f(r, y, z) = k.
(c) Consider the function g = f² (distance square). Find the partial derivatives (r, y, z) and
Buể (T, y, z). What do you notice?
(d) Let F(t) be a single-variable function. The following table gives some relevant values of this
function.
F
F'
F"
t = 0
-4
10
t = 1
13
-1
t = 2
-2
9.
-3
82h
aydz
Suppose that h(x, y, z) = F(g(x, Y, z)). Find values of (0,0, 2) and (0, 0, 2)
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