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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 f is a function, then

lim ( x , y ) ( 2 , 5 ) f ( x , y ) = f ( 2 , 5 )

To determine

Whether the statement “If f is a function, then lim(x,y)(2,5)f(x,y)=f(2,5) ” is true or false.

Explanation

The given statement is false since the below explanation disproves the given statement.

Let the function be f(x,y)=1(x2)2+(y5)2 .

Notice that the function is undefined when x = 2 or 5.

As (x,y)(2,5) , lim(x,y)(2,5)f(x,y) is,

lim(x

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Chapter 14 Solutions

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