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Does knowing that$$2|x y|-\frac{x^{2} y^{2}}{6}<4-4 \cos \sqrt{|x y|}<2|x y|$$tell you anything about$$\lim _{(x, y) \rightarrow(0,0)} \frac{4-4 \cos \sqrt{|x y|}}{|x y|} ?$$Give reasons for your answer.

2

Calculus 3

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Johns Hopkins University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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

01:55

$\lim _{x \rightarrow 0} \…

01:07

$$\lim _{x \rightarrow…

02:29

Use the Squeeze Theorem to…

in this question if x y greater than zero than the limit when X and Y approaches zero and zero to absolute X Y minus excess square Y square over six over absolute X y. If we simplified, we will get to X Y minus excess square Y square over six over X y, which will be equal to and the limit when X and Y approaches zero and zero for two absolute x y over absolute ex boy equals to and in case that X Y greater than or less than zero than the limit when X and why approaches zero and zero to absolute X Y minus access square. Why square over six over absolute X y, which will be equals also to and the other limit. Okay, when X and y approaches zero and zero on to absolute X Y over absolute X Y also will be equal to zero, also equal to two. So our limit when X and y approaches zero and 04 minus four co sign rule Absolute X Y over. Absolute X y will equal to what you think sandwich here

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