1. (5 pts.)True or False and give the reason why.
(a) Let h(x,y) be a continuous function. Then for any point (x0,y0) in the domain of h, the limit of h as (x,y) approach the point (x0,y0) exists.
(b) Let h(x,y) = x/y. The limit of h as (x,y) approach the point (1,1) exists.
(c) Let h(x,y) = x/y. The limit of h as (x,y) approach the point (0,0) exists.
(d) Let h(x,y) = { 3 (x,y) = (equal) (0,0).
{ 1 (x,y) != (not equal) (0,0).
The limit of h as (x,y) approach the point (0,0) doesn’t exist.
(e) Let h(x,y) = { 3 (x,y) = (0,0)
{ 1 (x,y) != (0,0).
The limit of h as (x,y) approach the point(0,0) is equal to 3.
(a) Let h(x,y) be a continuous function. Then for any point (x0,y0) in the domain of h, the limit of h as (x,y) approach the point (x0,y0) exists.
(b) Let h(x,y) = x/y. The limit of h as (x,y) approach the point (1,1) exists.
(c) Let h(x,y) = x/y. The limit of h as (x,y) approach the point (0,0) exists.
(d) Let h(x,y) = { 3 (x,y) = (equal) (0,0).
{ 1 (x,y) != (not equal) (0,0).
The limit of h as (x,y) approach the point (0,0) doesn’t exist.
(e) Let h(x,y) = { 3 (x,y) = (0,0)
{ 1 (x,y) != (0,0).
The limit of h as (x,y) approach the point(0,0) is equal to 3.
