1. For each of the following functions, find the maximal domain of

f, prove that the limit of f exists as (x, y) --4

(a, b), and find the value of that limit. (Note:

You can prove that the limit exists without using e'S and 8's-see Example 9.16.)

(a) (

X -1 )

f(x, y) = y _ l' x + 2 ,

(a,

b) = (1, -1).

(b) ( (

YSinX x 2 2 ) f x, y) = -x-, tan y' x + y - xy ,

(a,

b) = (0,1).

(c) (
X4 + y4 JfXYT)
f(x,y) = 2+ 2'{/2 2' X Y X +y (a,b) = (0,0).

(d) X _ (X2-1 X2Y -2XY + Y -(X-1)2)
f ( , y) - y2 + l' x2 + y2 - 2x - 2y + 2 '

(a,

b) = (1,1).