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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If fx(a, b) and fy(a, b) both exist, then f is differentiable at (a, b).

To determine

Whether the statement, “If fx(a,b)andfy(a,b) both exist, then f is differentiable at (a,b) ” is true or false.

Explanation

The given statement is false as the below example disproves the given statement.

Consider the function, f(x,y)={xyx2+y2if(x,y)(0,0)0if(x,y)=

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Chapter 14 Solutions

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