Let z = f(x, y).(a) Express z/x and z/y as limits.(b) In words, what do the derivatives

Chapter 13, Problem 8

(choose chapter or problem)

Let \(z=f(x, y)\).

(a) Express \(\partial z / \partial x\) and \(\partial z / \partial y\) as limits.

(b) In words, what do the derivatives \(f x(x 0, y 0)\) and \(f y(x 0, y 0)\) tell you about the surface \(z=f(x, y)\)?

(c) In words, what do the derivatives \(\partial z / \partial x(x 0, y 0)\) and \(\partial z / \partial y(x 0, y 0)\) tell you about the rates of change of z with respect to x and y?

Equation Transcription:

 

Text Transcription:

Partial z/Partial x

Partial z/Partial y

 fx (x0, y0)

fy (x0, y0)

z = f(x, y)

Partial z/Partial x(x0, y0)

Partial z/Partial y(x0, y0)