/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 Describe the domain and range of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 20

Describe the domain and range of the function. $$ f(x, y)=\arccos (y / x) $$

Short Answer

Expert verified
The domain of the function are all pairs (x, y) in the real numbers, such that \(-x \leq y \leq x\) for \(x > 0\) and \(x \leq y \leq -x\) for \(x < 0\). Pairs of the form (0, y) are excluded. The range of the function is between 0 and \(\pi\).

Step by step solution

01

Define the domain

First, recognize that for the function \(f(x, y)=\arccos (y / x)\), \(y/x\) must be between -1 and 1 inclusive for the function to be defined. And also \(x\neq 0\). Therefore, the domain of the function are all pairs (x, y) in the real numbers, such that \(-x \leq y \leq x\) for \(x > 0\) and \(x \leq y \leq -x\) for \(x < 0\). No restrictions on y when x=0, hence pairs of the form (0, y) for any y are excluded.
02

Define the range

Since this is an arccosine function, we also know that the range is between 0 and \(\pi\). The arccosine function only returns these values.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Differentiate implicitly to find the first partial derivatives of \(w\). \(x^{2}+y^{2}+z^{2}-5 y w+10 w^{2}=2\)

In Exercises 51-58, differentiate implicitly to find the first partial derivatives of \(z\) \(x^{2}+y^{2}+z^{2}=25\)

Describe the difference between the explicit form of a function of two variables \(x\) and \(y\) and the implicit form. Give an example of each.

Show that the function is differentiable by finding values for \(\varepsilon_{1}\) and \(\varepsilon_{2}\) as designated in the definition of differentiability, and verify that both \(\varepsilon_{1}\) and \(\varepsilon_{2} \rightarrow 0\) as \((\boldsymbol{\Delta x}, \boldsymbol{\Delta} \boldsymbol{y}) \rightarrow(\mathbf{0}, \mathbf{0})\) \(f(x, y)=5 x-10 y+y^{3}\)

In Exercises \(43-46,\) find \(\partial w / \partial s\) and \(\partial w / \partial t\) by using the appropriate Chain Rule. \(w=x y z, \quad x=s+t, \quad y=s-t, \quad z=s t^{2}\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.