Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q 19. (page 916)

In Exercise, provide a rough sketch of the graph of a function of two variables with the specified level “curve(s).”

Some level curves consist of two concentric circles.

Short Answer

Expert verified

Some level curves consist of two concentric circles.

Step by step solution

01

Step 1. Given information

Some level curves consist of two concentric circles.

02

Step 2. Explanation

The goal is to draw a rough drawing of the graph of a two-variable function with "all level curves being circles except one, which is a point."

The graph must have a single point at a value of z to have a single point as one of the level curves.

A right circular cone is one of the examples.

The following is an example of a rough sketch.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y)=xsin⁡y,P=3,π2

In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.

f(x,y,z)=x+y+zwhenx2+y2+z2=9

Use Theorem 12.32 to find the indicated derivatives in Exercises 21–26. Express your answers as functions of a single variable. dxdtwhenx=rcosθ,r=t2−5,andθ=t3+1

In Exercises 37-42, use the partial derivatives of role="math" localid="1650186824938" fx,y=xyand the point e,3specified to

afind the equation of the line tangent to the surface defined by the function in the xdirection,

bfind the equation of the line tangent to the surface defined by the function in the ydirection, and

cfind the equation of the plane containing the lines you found in parts aand b.

Gradients: Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y,z)=x2yz,P=(0,3,−1)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.

Sign-up for free