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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the limit if it exists, or show that the limit does not exist.

19. lim ( x , y , z ) ( π , 0 , 1 / 3 ) e y 2 tan ( x z )

To determine

To find: The limit of the function lim(x,y,z)(π,0,13)ey2tan(xz) if exist; otherwise show that the limit does not exist.

Explanation

Notice that the functions y2 and xy are polynomial functions.

Since every polynomial function is continuous, the functions ey2 and xz are continuous.

Hence the given composition function ey2tan(xz) is continuous as tan(xz) is continuous for xzπ2+nπ .

As the given function is continuous, substitute x=π , y = 0 and z=13 directly in the given function and obtain the required limit

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Chapter 14 Solutions

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