Q.20 Using聽Theorem聽12.31聽as聽a聽mo... [FREE SOLUTION]

Chapter 12: Q.20 (page 953)

$U \sin g T h e o r e m 12.31 a s a m o d e l, p r o v i d e a c o n j e c t u r e y o u t h i n k w o u l d b e s u f f i c i e n t t o g u a r a n t e e t h a t a f u n c t i o n o f n v a r i a b l e s i s d i f f e r e n t i a b l e a t a p o i n t i n i t s d o m a i n .$

Short Answer

Expert verified

The function variables is differntlable at a point in its domain

Step by step solution

Introduction

$W e h a v e g i v e n f (x, y) = 3 x^{2} - 4 x y - 2 y^{2} a t s p e c i f i e d p o i n t P = (0, 0) w i t h u n i t v e c t o r u = (1, 1)$

Step 2 Directional derivative of function at point P with directional unit vector u is given by,

$鈭� f (P) 路 u = 鈭� f (0, 0) 路 u = ({\frac{d f}{d x}|}_{(0, 0)} i + {\frac{d f}{d y}|}_{(0, 0)} j) 路 (\frac{i + j}{\sqrt{i^{2} + j^{2}}})$

$= [(6 x - 4 y)_{(0, 0)} i + (- 4 x - 4 y)_{(0, 0)} j] 路 (\frac{i + j}{\sqrt{2}})$

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

$U \sin g T h e o r e m 12.31 a s a m o d e l, p r o v i d e a c o n j e c t u r e y o u t h i n k w o u l d b e s u f f i c i e n t t o g u a r a n t e e t h a t a f u n c t i o n o f n v a r i a b l e s i s d i f f e r e n t i a b l e a t a p o i n t i n i t s d o m a i n .$

Short Answer

Step by step solution

Introduction

Step 2 Directional derivative of function at point P with directional unit vector u is given by,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Geometry

Decision Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

UsingTheorem12.31asamodel,provideaconjectureyouthinkwouldbesufficienttoguaranteethatafunctionofnvariablesisdifferentiableatapointinitsdomain.

Short Answer

Step by step solution

Introduction

Step 2 Directional derivative of function at point P with directional unit vector u is given by,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Geometry

Decision Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

$U \sin g T h e o r e m 12.31 a s a m o d e l, p r o v i d e a c o n j e c t u r e y o u t h i n k w o u l d b e s u f f i c i e n t t o g u a r a n t e e t h a t a f u n c t i o n o f n v a r i a b l e s i s d i f f e r e n t i a b l e a t a p o i n t i n i t s d o m a i n .$