1. Let 1 f(x, y) = 1-x² - y² (a) Find the domain D of f and show that f is of class C on D. (b) Show that f is analytic at (0, 0), i.e., show that f can be expanded into a Taylor series at (0, 0) which converges to f in some neighborhood U of the origin. Find the largest such neighborhood U. (c) Compute a¹ f Əx¹ əy³ (0,0).
1. Let 1 f(x, y) = 1-x² - y² (a) Find the domain D of f and show that f is of class C on D. (b) Show that f is analytic at (0, 0), i.e., show that f can be expanded into a Taylor series at (0, 0) which converges to f in some neighborhood U of the origin. Find the largest such neighborhood U. (c) Compute a¹ f Əx¹ əy³ (0,0).
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:1. Let
1
f(x, y) =
1-x² - y²
(a) Find the domain D of f and show that f is of class C on D.
(b) Show that f is analytic at (0, 0), i.e., show that f can be expanded into a Taylor series
at (0, 0) which converges to f in some neighborhood U of the origin. Find the largest
such neighborhood U.
(c) Compute
a¹ f
əx¹ əy³
(0,0).
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