12.1  Limits and Continuity of multi-variable functions 1-6. Find the limit, if it exists, or show that the limit does not exist.

1. .

http://matrix.skku.ac.kr/cal-lab/cal-12-1-1.html (Sol) 0 0

Limit  exists and is 0.

2. http://matrix.skku.ac.kr/cal-lab/cal-12-1-2.html (Sol) 1 -1

Limit does not exist.

3. .

http://matrix.skku.ac.kr/cal-lab/cal-12-1-3.html (Sol) 0 0

Limit  exists and is 0.

4. .

http://matrix.skku.ac.kr/cal-lab/cal-12-1-4.html (Sol) 0 0

Limit  exists and is 0.

5. .

http://matrix.skku.ac.kr/cal-lab/cal-12-1-5.html (Sol) 0 0

Limit  exists and is 0.

6. .

http://matrix.skku.ac.kr/cal-lab/cal-12-1-6.html (Sol) 0

So  0

0

Limit  exists and is 0.

7-8. Let each of the following functions have the value 0 at the origin. Which of them are conti. at the origin?

7. .

http://matrix.skku.ac.kr/cal-lab/cal-12-1-7.html (Sol) 0 0

Limit  exists and is 0.

So it is conti at the origin.

8. http://matrix.skku.ac.kr/cal-lab/cal-12-1-8.html (Sol) +Infinity

Limit does not exist.

So it is not conti at the origin.

9-10. Find and the set on which is continuous.

10. , .

(Sol)  is continuous.

11. , .

(Sol)  is continuous.