/*! 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. 13 What does it mean for a function... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q. 13 (page 953)

What does it mean for a function of two variables, f(x,y), to be differentiable at a point (a,b)?

Short Answer

Expert verified

f(x,y)to be differentiated at some extent (a,b)when it on an open set containing the purpose and if 鈭�f(x,y)=f(a+螖x,b+螖y)-f(a,b)be a function of (x,y).

Step by step solution

01

Differentiability.

A differentiable function of one real variable is 1whose derivative occurs at each point in its domain, per mathematics.

In other words, each interior point within the domain of a differentiable function includes a non-vertical tangent line on its graph.

02

Differentiability for two functions of variables.

Let f(x,y)be a function of two variables defined on an open set containing the purpose(a,b), and and let 鈭�f(x,y)=f(a+螖x,b+螖y)-f(a,b)be a function (x,y).

If the partial derivativesfx(a,b)and fy(a,b)both exist, the function f is claimed to be differentiable at (a,b).

鈭�f(x,y)=fx(a,b)螖x+fy(a,b)螖y+系1螖x+系2螖y

where 系1and 系2are 鈭�xand 鈭�yfunctions, and both move to zero when(鈭�x,鈭�y)鈫�(0,0)

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

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

f(x,y)=x+yx2+y2,P=(1,2),v=鉄�3,鈭�2鉄�

Evaluate the following limits, or explain why the limit does not exist.

lim(x,y)鈫�(0,0)x3+y3x2+y2

Extrema: Find the local maxima, local minima, and saddle points of the given functions.

f(x,y)=2x2+y2+y+5.

In Exercises 24鈥�32, find the maximum and minimum of the functionf subject to the given constraint. In each case explain why the maximum and minimum must both exist.

f(x,y,z)=xyzwhenx2+4y2+16z2=64

Explain the steps you would take to find the extrema of a function of two variables, f(x,y),if(x,y)is a point in the rectangle Rdefined by role="math" localid="1649881836115" a鈮�x鈮�bandc鈮�y鈮�d.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.