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Q23E

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Essential Calculus: Early Transcendentals

Found in: Page 632

Book edition 2nd

Author(s) James Stewart

Pages 830 pages

ISBN 9781133112280

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Short Answer

Determine the set of points at which the function is continuous.
\(G(x,y) = \ln ({x^2} + {y^2} - 4)\)

\(\{ (x,y){\rm{ : }}{x^2} + {y^2} > 4\} \)

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Recognizing the form of Equation / Function:

The given function \(G(x,y) = \ln \left( {{x^2} + {y^2} - 4} \right)\)

The given function is a logarithmic function.

Step 2: The function is not defined when \({x^2} + {y^2} - 4 \le 0\) that is when \({x^2} + {y^2} \le 4\)

Hence G(x, y) is continuous everywhere except when \({x^2} + {y^2} \le 4\)

That is G(x, y) is defined on the set

\(\{ (x,y){\rm{ : }}{x^2} + {y^2} > 4\} \)

Most popular questions for Math Textbooks

Determine the values of \(\frac{{\partial z}}{{\partial s}}\)and \(\frac{{\partial z}}{{\partial t}}\) using chain rule if \(z = {e^r}\cos \theta ,r = st\) and \(\theta = \sqrt {{s^2} + {t^2}} {\rm{. }}\)

Use polar coordinates to find the limit. If \((r,\theta )\) are polar coordinates of the point \((x, y)\) with \(r \ge 0\) note that \(r \to {0^ + }\) as \((x,y) \to (0,0)\)

\(\mathop {lim}\limits_{(x,y) \to (0,0)} \left( {{x^2} + {y^2}} \right)\ln \left( {{x^2} + {y^2}} \right)\)

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Let \(g(x,y) = \cos (x + 2y)\)

Evaluate \(g(2, - 1)\)
Find the domain of g
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\(f(x,y,z) = \arcsin ({x^2} + {y^2} + {z^2})\)

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