/*! 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} Q 5. Let f:R3鈫扲聽be a function of t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q 5. (page 915)

Let f:R3鈫�Rbe a function of three variables. Explain why the graph of f is a subset of R4.

Short Answer

Expert verified

The graph of f is a subset of R4as it is plotted using four axes: x, y, z and w.

Step by step solution

01

Step 1. Given information

Function isf:R3鈫�R

02

Step 2. Explanation

A graph is a graphic representation that shows between input and output variables.

The input and output values are used to plot the graph of a function.

For the function w=fx,y,z, graph is to be plotted between four variables, ' x,y,z,w

Thus, the graph will have four axes to plot.

This is the definition of R4

Hence, the graph of f must be a subset ofR4

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

Achainruleforfunctionsoftwovariables:Letf(x,y)=x2y3,x=scost,andy=ssint.Find鈭�f鈭�xand鈭�f鈭�y.

Explain the steps you would take to find the extrema of a function of two variablesf(x,y),if (x,y)is a point in a triangle role="math" localid="1649884242530" Tin the xy-plane.

In Exercises, by considering the function f(x,y)=x2ysubject to the constraint x+y=0,you will explore a situation in which the method of Lagrange multipliers does not provide an extremum of a function.

Explain why(0,0)is not an extremum of f(x,y)=x2ysubject to the constraintx+y=0.

Describe the meanings of each of the following mathematical expressions:

fzx0,y0,z0

Solve the exact differential equations in Exercises 63鈥�66.exlny+x3+exydydx=0
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

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.