Let n e N, let U C R" be open and let f : U → R be partially differentiable. Assume that there exists M E (0,+0) , such that |Ə;f (x)| < M Vx e U, i e {1,2,...,n}. Show that f is uniformly continuous.

Let n e N, let U C R" be open and let f : U → R be partially differentiable. Assume that there exists M E (0,+0) , such that |Ə;f (x)| < M Vx e U, i e {1,2,...,n}. Show that f is uniformly continuous.

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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Equations and inequalities describe the relationship between two mathematical expressions.

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Let n e N, let u c R" be open and let f : U → R be
partially differentiable. Assume that there exists M E (0, +∞) , such that
|Ə;f(x)| < M
Vx e U, i e {1,2,...,n}.
Show that f is uniformly continuous.

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