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Gives a function $f(x, y)$ and a positive number $\epsilon$ In each exercise, show that there exists a $\delta > 0$ such that for all $(x, y)$$$\sqrt{x^{2}+y^{2}} < \delta \Rightarrow|f(x, y)-f(0,0)| < \epsilon$$$$f(x, y)=(x+y) /(2+\cos x), \quad \epsilon=0.02$$

$\sqrt{x^{2}+y^{2}}<\delta \Rightarrow|f(x, y)-f(0,0)|<\epsilon$

Calculus 3

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Johns Hopkins University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

04:47

Gives a function $f(x, y)$…

03:20

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