Q 50. Determine the domains of the fun... [FREE SOLUTION]

Chapter 12: Q 50. (page 932)

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

Short Answer

Expert verified

The function $f (x, y, z) = \ln (x^{2} + y^{2} + z^{2})$ is continuous on the set $\{(x, y, z) 鈭� f^{3} : x^{2} + y^{2} + z^{2} > 0\}$ .

Step by step solution

Step 1. Given information.

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

Determine the domains of the functions.

Consider the function: $g : f^{3} 鈫� f$ .Then the domain of the function $g$ is defined as

$D o m a i n (g) = \{(x, y, z) 鈭� f^{3} : g (x, y, z)\}$

Since the domain of the natural logarithm $\ln (x)$ is the set $\{x 鈭� f : x > 0\}$ .

$l n (x^{2} + y^{2} + z^{2})$ is defined on the set $\{(x, y, z) 鈭� f^{3} : x^{2} + y^{2} + z^{2} > 0\}$ .

Here from the above statement, the domain of the function is role="math" localid="1653402193440" $f (x, y, z) = \ln (x^{2} + y^{2} + z^{2})$ is

$D o m a i n (f) = \{(x, y, z) 鈭� f^{3} : x^{2} + y^{2} + z^{2} > 0\}$

Step 3. To find continuous of the function.

Since the natural logarithm is continuous on the entire domain, therefore the function $f (x, y, z) = \ln (x^{2} + y^{2} + z^{2})$ is continuous on the set $\{(x, y, z) 鈭� f^{3} : x^{2} + y^{2} + z^{2} > 0\}$

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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.
$f (x, y, z) = \ln (x^{2} + y^{2} + z^{2})$

Short Answer

Step by step solution

Step 1. Given information.

Determine the domains of the functions.

Step 3. To find continuous of the function.

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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,z)=ln(x2+y2+z2)

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

Statistics

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

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.
$f (x, y, z) = \ln (x^{2} + y^{2} + z^{2})$