2. [14.1: Functions of Several Variables] Match the functions z = f(x,y) with the surfaces representing their graphs. Provide a written explanation for your answers. (The origin is in the middle of each box. The figures only show that portion of the surface that is inside a box.) (a) f(x,y) = x² + y² (b) f(x, y) = x² +x³y² (c) f(x,y) = (x² – y²) exp(-x² – y²) (d) f(x, y) = sin(x² + 2y²) (e) f(x,y) = x² exp(-x²) – exp(-y²) (f) f(x,y) = x - y

2. [14.1: Functions of Several Variables] Match the functions z = f(x,y) with the surfaces representing their graphs. Provide a written explanation for your answers. (The origin is in the middle of each box. The figures only show that portion of the surface that is inside a box.) (a) f(x,y) = x² + y² (b) f(x, y) = x² +x³y² (c) f(x,y) = (x² – y²) exp(-x² – y²) (d) f(x, y) = sin(x² + 2y²) (e) f(x,y) = x² exp(-x²) – exp(-y²) (f) f(x,y) = x - y

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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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

2. [14.1: Functions of Several Variables] Match the functions z = f(x, y) with the surfaces
representing their graphs. Provide a written explanation for your answers. (The origin is
in the middle of each box. The figures only show that portion of the surface that is inside a
box.)
(a) f(x,y)
x? + y?
(b) f(x, y)
x2 + x³y?
(c) f(x, y) = (x2 - y?) exp(-x? - y²)
(d) f(x, y)
sin(x? +2y?)
(e) f(x, y)
x? еxp(-x?) - еxp(-у?)
(f) f(x, y) = x - y
I
II
III
IV
V
VI
VII
VIII
IX
X

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