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Calculus / Calculus: Early Transcendentals 1 / Chapter 12.3 / Problem 46E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Solved: Limits of functions of three variables Evaluate

Chapter 9, Problem 46E

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QUESTION:

Limits of functions of three variables Evaluate the following limits.

\(\lim _{(x, y, z) \rightarrow(1,1,1)} \frac{x-\sqrt{x z}-\sqrt{x y}+\sqrt{y z}}{x-\sqrt{x z}+\sqrt{x y}-\sqrt{y z}}\)

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QUESTION:

Limits of functions of three variables Evaluate the following limits.

\(\lim _{(x, y, z) \rightarrow(1,1,1)} \frac{x-\sqrt{x z}-\sqrt{x y}+\sqrt{y z}}{x-\sqrt{x z}+\sqrt{x y}-\sqrt{y z}}\)

ANSWER:

Solution 46E

Step 1:

Given equation is

$\lim\limits_{{(x,y,z)\ } \rightarrow {\ (\ 1,1,1)}}$ $\frac{x\ -\ \ \sqrt{\ x\ z\ }-\ \sqrt{\ x\ y\ }\ +\ \sqrt{\ y\ z}}{x\ -\ \sqrt{\ x\ z\ }+\ \sqrt{\ x\ y\ }\ -\ \sqrt{\ y\ z}}$

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