Engineering Calculus Notes 302

Engineering Calculus Notes 302 - Theorem for real-valued...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
290 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION derivative of the restriction (which is nothing other than a partial of φ ( x,y )) is the appropriate ratio of partials of f , as given in Equation ( 3.24 ). But then, rather than trying to prove directly that φ is diFerentiable as a function of two variables, we can appeal to Theorem 3.3.4 to conclude that, since its partials are continuous, the function is diFerentiable. This concludes the proof of the Implicit ±unction
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Theorem for real-valued functions of three variables. As an example, consider the level surface (igure 3.15 ) L ( f, 1), where x y z b (1 , 1 , 2) b (0 , 1 , 0) igure 3.15: The Surface L ( 4 x 2 + y 2 z 2 , 1 ) f ( x,y,z ) = 4 x 2 + y 2 z 2 : The partial derivatives of f ( x,y,z ) are f x ( x,y,z ) = 8 x f y ( x,y,z ) = 2 y f z ( x,y,z ) = 2 z ;...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online