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Suppose that the function f: R" → R satisfies f()| ≤ C|||| +r for = (1, 2,,m) ER". 02 (a) Find f(0) and the first-order partial derivatives (0) for each i = 1, 2,..., m. (b) Show that f is differentiable at 0. for some a > 1, where ||||= √x + x + ...

Suppose that the function f: R" → R satisfies f()| ≤ C|||| +r for = (1, 2,,m) ER". 02 (a) Find f(0) and the first-order partial derivatives (0) for each i = 1, 2,..., m. (b) Show that f is differentiable at 0. for some a > 1, where ||||= √x + x + ...

Advanced Engineering Mathematics
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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Suppose that the function f: Rm → R satisfies |f()| ≤C|||| for some a > 1, where |||| = √x + x2 + + x² for = (1, 2,.,m) € R™. .. (a) Find f(0) and the first-order partial derivatives of (0) for each i = 1,2,..., m. (b) Show that f is differentiable at 0.
Transcribed Image Text:Suppose that the function f: Rm → R satisfies |f()| ≤C|||| for some a > 1, where |||| = √x + x2 + + x² for = (1, 2,.,m) € R™. .. (a) Find f(0) and the first-order partial derivatives of (0) for each i = 1,2,..., m. (b) Show that f is differentiable at 0.
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