The values of f x ( 0 , y ) by calculating the limit lim h → 0 ( f ( h , y ) − f ( 0 , y ) h ) where function f is defined as f ( x , y ) = { x y ( x 2 − y 2 ) x 2 + y 2 , for ( x , y ) ≠ ( 0 , 0 ) 0 , for ( x , y ) = ( 0 , 0 ) .

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Answer 1

Question

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

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Answer 2

Question

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

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Answer 3

Question

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

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Answer 4

Question

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

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Answer 5

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

Answer 6

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

Answer 7

Chapter 6.2, Problem 69E

(a)

To determine

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

Answer 8

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

Answer 9

(b)

To determine

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

Answer 10

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

Answer 11

(c)

To determine

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

Answer 12

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Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 6.1 - Forf(x,y)=x23xy,find(0,2),f(2,3),andf(10,5).Ch. 6.1 - 2. . Ch. 6.1 - 3. . Ch. 6.1 - 4. . Ch. 6.1 - Forf(x,y)=Inx+y3,findf(e,2),f(e2,4),andf(e3,5).Ch. 6.1 - 6. . Ch. 6.1 - Forf(x,y,z)=x2y2+z2,findf(1,2,3)andf(2,1,3).Ch. 6.1 - 8. . Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...

The values of f x ( 0 , y ) by calculating the limit lim h → 0 ( f ( h , y ) − f ( 0 , y ) h ) where function f is defined as f ( x , y ) = { x y ( x 2 − y 2 ) x 2 + y 2 , for ( x , y ) ≠ ( 0 , 0 ) 0 , for ( x , y ) = ( 0 , 0 ) .

Solution Summary: The author calculates the value of function f_x(0,y) by calculating the limit.

Concept explainers

To calculate: The values of $fx(0,y)$ by calculating the limit $limh→0(f(h,y)−f(0,y)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

To calculate: The values of $fy(x,0)$ by calculating the limit $limh→0(f(x,h)−f(x,0)h)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ .

To calculate: The values of the function $fyx(0,0)$ and $fxy(0,0)$ where function f is defined as $f(x,y)={xy(x2−y2)x2+y2,for (x,y)≠(0,0)0 , for (x,y)=(0,0)$ and also compare $fyx(0,0)$ and $fxy(0,0)$ for given function.

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