For each of the following statements, decide whether it is true or false, and justify your answer: (a) Two different level curves of a function f(x, y) can intersect. (b) For every function f(x, y) and every real number K, the level curve f(x, y) = K exists (and is non-empty). (c) If f is a function of x and y, and fry = 0, then either fr = 0 or fy = 0. (d) If f(x, y) is a function such that • f(0,0) = 0 • There exists e > 0 such that f(x, y) = 2x when y = 0 and –e < x < e (i.e. for values of x close to 0) then fr(0,0) = 2. %3D
For each of the following statements, decide whether it is true or false, and justify your answer: (a) Two different level curves of a function f(x, y) can intersect. (b) For every function f(x, y) and every real number K, the level curve f(x, y) = K exists (and is non-empty). (c) If f is a function of x and y, and fry = 0, then either fr = 0 or fy = 0. (d) If f(x, y) is a function such that • f(0,0) = 0 • There exists e > 0 such that f(x, y) = 2x when y = 0 and –e < x < e (i.e. for values of x close to 0) then fr(0,0) = 2. %3D
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:For each of the following statements, decide whether it is true or false, and
justify your answer:
(a) Two different level curves of a function f(x, y) can intersect.
(b) For every function f(x, y) and every real number K, the level curve f(x, y) = K exists
(and is non-empty).
(c) If f is a function of x and y, and fry = 0, then either fr = 0 or fy = 0.
(d) If f(x, y) is a function such that
• f(0,0) = 0
• There exists e > 0 such that f(x, y) = 2x when y = 0 and –e < x < e (i.e. for values
of x close to 0)
then fr(0,0) = 2.
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