Question

how can i solve " lim x sin 1/y" (x,y) (0,0)

Answer 1

as x approaches what?

Answer 2

x,y approaches to (0,0)

Answer 3

I got the answer that limit doesn't exist..

Answer 4

can you explain that how you solve it?

Answer 5

okay let me recall how to do this.. i used a calculator for this..give me a few minutes..

Answer 6

http://www.youtube.com/watch?v=_ges8Z6DZkc
watching this video haha..

Answer 7

okay so here's the deal, you have to prove that limit of that doesn't exist, or if you approach 0,0 from one function, limit is something and if you approach it from some other function limit is something else..

Answer 8

First of all:
Let's approach along the y=1.
Approaching along y=1 means:
y = 1, x - varies, so:
Limit as (x,y)->(0,0) x * Sin(1/y) = x * Sin(1/1) = 0 * Sin1 = 0

Answer 9

Now let's approach along the x = 1 axis:
x = 1, y - varies:
Limit as (x,y) -> (0,0) x*Sin(1/y) = 1 * Sin(1/y) , which is basically limit as y->0 of Sin(1/y)

Answer 10

and that is undefined..

Answer 11

This means that the limit does not exist.

Answer 12

It is usually impossible to find the limit in multivar calculus, because there are so many ways to approach the values, so all you need to do is get two cases that are different, like the cases above..

Answer 13

And limit as y->0 of Sin (1/y) does not exist, you can't do anything with the y in the denominator inside the Sin..

Answer 14

thanks a lot :)

Answer 15

Can you then please click on Good Answer? Thanks =)

Answer 16

i am sorry i do not know where is the button that show good answer!

Answer 17

Right above any of my posts:
It says bahrom7893 Group Superstar ...................... Good Answer (in blue and white)