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### Essential Calculus: Early Transcendentals

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

See the step by step solution

## 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, $$f(3,1) = 6$$.