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Q1E

Expert-verifiedFound in: Page 632

Book edition
2nd

Author(s)
James Stewart

Pages
830 pages

ISBN
9781133112280

**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, \(f(3,1) = 6\).

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 \(\mathop {\lim }\limits_{x \to c} f(x) = f(c)\).

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, \(f(3,1) = 6\).

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