   Chapter 14, Problem 5RCC

Chapter
Section
Textbook Problem

(a) Write expressions for the partial derivatives fx(a, b) and fy(a, b) as limits.(b) How do you interpret fx(a, b) and fy(a, b) geometrically? How do you interpret them as rates of change?(c) If f(x, y) is given by a formula, how do you calculate fx and fy?

(a)

To determine

To state: The expressions for the partial derivatives fx(a,b) and fy(a,b) as limits.

Explanation

By the definition, it is clear that the first order partial derivative with respect to x at (a,b) is given as, when h0 .

fx(a,b)=limh0f(a+h,b)f(a,b)h

(b)

To determine

To interpret: The functions of fx(a,b),fy(a,b) geometrically and the rates of change.

(c)

To determine

To calculate: The values of fx and fy by using the formula of f(x,y) .

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