Q 49. 聽Determine the domains of the f... [FREE SOLUTION]

Chapter 12: Q 49. (page 932)

Determine the domains of the functions in Exercises 47鈥�56, and find where the functions are continuous.
$f (x, y) = \sqrt{x^{2} + y}$

Short Answer

Expert verified

The function $f (x, y) = \sqrt{x^{2} + y}$ is continuous on the setlocalid="1653390182338" role="math" $\{(x, y) 鈭� f^{2} : y 鈮� - x^{2}\}$ .

Step by step solution

Step 1. Given information.

We have given expression: $f (x, y) = \sqrt{x^{2} + y}$

Determine the domains of the functions.

Consider the function: $g : f^{2} 鈫� f$ Then the domain of the function is

$D o m a i n (g) = \{(x, y) 鈭� f^{2} : g (x, y) i s d e f i n e d\}$

Since the rational function $f (x, y) = \sqrt{x^{2} + y}$ assumes real values of all $(x, y) 鈭� f^{2}$ such that.

$x^{2} + y 鈮� 0 y 鈮� - x^{2}$

The domain of the function islocalid="1653327001783" $D o m a i n (f) = \{(x, y) 鈭� f^{2} : y 鈮� - x^{2}\}$ .

Step 3. To find continuous of the function.

Since $x^{2} + y$ being a polynomial function of two variable is continuous for every point on $f^{2}$ .

The rational function is continuous for every point on $f^{2}$ where $\sqrt{x^{2} + y}$ is defined.

Since the square of the real number can never be negative, therefore $x^{2} 鈮� - y$ .

Hence the function $f (x, y) = \sqrt{x^{2} + y}$ is continuous on the set $\{(x, y) 鈭� f^{2} : y > - x^{2}\}$

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91影视

Determine the domains of the functions in Exercises 47鈥�56, and find where the functions are continuous.
$f (x, y) = \sqrt{x^{2} + y}$

Short Answer

Step by step solution

Step 1. Given information.

Determine the domains of the functions.

Step 3. To find continuous of the function.

One App. One Place for Learning.

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91影视

Determine the domains of the functions in Exercises 47鈥�56, and find where the functions are continuous.f(x,y)=x2+y

Short Answer

Step by step solution

Step 1. Given information.

Determine the domains of the functions.

Step 3. To find continuous of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Applied Mathematics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Determine the domains of the functions in Exercises 47鈥�56, and find where the functions are continuous.
$f (x, y) = \sqrt{x^{2} + y}$