Calculus: Early Transcendentals, Loose-Leaf Version

8th Edition

ISBN: 9781305272354

Author: James Stewart

Publisher: Brooks Cole

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Textbook Question

Chapter 14.4, Problem 46E

(a) The function

f ( x , y ) = { x y x 2 + y 2 if ( x , y ) ≠ (0, 0) 0 if ( x , y ) = (0, 0)

was graphed in Figure 4. Show that f_x(0, 0) and f_y(0, 0) both exist but f is not differentiable at (0, 0). [Hint: Use the result of Exercise 45.]

(b) Explain why f_x and f_y are not continuous at (0, 0).

Chapter 14.4, Problem 46E, (a) The function f(x,y)={xyx2+y2if(x,y)(0,0)0if(x,y)=(0,0) was graphed in Figure 4. Show that fx(0,

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Chapter 14.4, Problem 45E

Chapter 14.5, Problem 1E

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Chapter 14 Solutions

Calculus: Early Transcendentals, Loose-Leaf Version

Ch. 14.1 - In Example 2 we considered the function W = f(T,...Ch. 14.1 - The temperature-humidity index I (or humidex, for...Ch. 14.1 - Prob. 3E Ch. 14.1 - Verify for the Cobb-Douglas production function...Ch. 14.1 - A model for the surface area of a human body is...Ch. 14.1 - The wind-chill index W discussed in Example 2 has...Ch. 14.1 - The wave heights h in the open sea depend on the...Ch. 14.1 - A company makes three sizes of cardboard boxes:...Ch. 14.1 - Let g(x, y) = cos(x + 2y). (a) Evaluate g(2, 1)....Ch. 14.1 - Let F(x,y)=1+4y2. (a) Evaluate F(3,1). (b) Find...

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Chapter 14 Solutions