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Found in: Page 632

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# 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 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

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

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