Q.13 What does it mean for a function... [FREE SOLUTION]

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

Differentiability at the point of function for two variables is $螖 x$ and $鈭� y,$ and both goes to zero as $(鈭� x, 鈭� y) 鈫� (0, 0) .$

Step by step solution

Introduction

Differentiability for function of two variables

$f (x, y)$ be a function of two variables defined on an open set containing the point $(a, b) .$ and let $鈭� f (x, y) = f (a + 螖 x, b + 螖 y) - f (a, b)$ The function $f$ is said to be differentiable at

$(a, b)$ if the partial derivative $f_{x} (a, b)$ and $f_{y} (a, b)$ both exist and

$鈭� f (x, y) = f_{x} (a, b) 螖 x + f_{y} (a, b) 螖 y + 系_{1} 螖 x + 系_{2} 螖 y$

Solution

Where $蔚_{1}$ and $蔚_{2}$ are function of $螖 x$ and $螖 y$ , and both goes to zero as $(螖 x, 螖 y) 鈫� (0, 0)$ .

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Introduction

Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Statistics

Geometry

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

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

Short Answer

Step by step solution

Introduction

Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Statistics

Geometry

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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