Chapter 17.1, Problem 29E

(a)

To determine

To find: The expression $\frac{f\left(x+h,y\right)-f(x,y)}{h}$.

(b)

To determine

To find: The expression $\frac{f\left(x,y+h\right)-f(x,y)}{h}$.

(c)

To determine

To find: The limit value of $\underset{h\to 0}{\lim }\frac{f\left(x+h,y\right)-f(x,y)}{h}$.

(d)

To determine

To find: The limit value of $\underset{h\to 0}{\lim }\frac{f\left(x,y+h\right)-f(x,y)}{h}$.