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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 + ...

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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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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