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Essential Calculus: Early Transcendentals
Found in: Page 632
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

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

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Short Answer

suppose that \(\mathop {lim}\limits_{\left( {x,y} \right) \to \left( {3,1} \right)} f(x,y) = 6\) . What can you say about the value of \(f(3,1)\)? What if f is continuous?

The value of\(f(3,1)\)is\(6\). If the function f is continuous then, \(f(3,1) = 6\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Definition of the continuous function

Suppose the function f is a real function on a subset of the real numbers and let c be a point in the domain of f. then f is continuous at c if \(\mathop {\lim }\limits_{x \to c} f(x) = f(c)\).

Step 2: Find the value of \(f(3,1)\)

We are given that \(\mathop {\lim }\limits_{(x,y) \to (3,1)} f(x,y) = 6\)

Here, \((x,y)\) approaches to \((3,1)\). Thus the value is \(6\).

According to the definition of the continuous function, if f is continuous then the value of \(f(3,1) = 6\) .

Therefore, The value of\(f(3,1)\)is\(6\). If the function f is continuous then, \(f(3,1) = 6\).

Most popular questions for Math Textbooks

Explain why each function is continuous or discontinuous.

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

\(\mathop {lim}\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} \frac{{{y^2}si{n^2}x}}{{{x^4} + {y^4}}}\)
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