Limit in Two Variables: Approaching the 0/0 Case

[tysonk]

How do I approach such question,
0/0 case in two variables, I can't find a simplification.

Thanks for the help.

 

[Dick]

Look for two ways to approach (0,0) that will give you different limits. That will prove the limit doesn't exist and you don't have to worry about it anymore.

 

[veneficus5]

isn't it -1?

edit: oh got it

2nd edit: nope still got -1

I approached from both possible y's

 

[Dick]

isn't it -1?

edit: oh got it

2nd edit: nope still got -1

I approached from both possible y's

Look at the limit as y->0 when x=0 and the limit as x->0 when y=0.

 

[tysonk]

I learned that one can plug in things like y=x, y=2x to help determine whether a limit can exist. If a different value is obtained then a limit may not exist.
Is it still possible to plug in y=x^3

Because when we plug in y=x and y=x^3 we get different values. Thanks.

 

[Dick]

I learned that one can plug in things like y=x, y=2x to help determine whether a limit can exist. If a different value is obtained then a limit may not exist.
Is it still possible to plug in y=x^3

Because when we plug in y=x and y=x^3 we get different values. Thanks.

Sure. That works. I still think x=0 and y=0 are easier, but it's your choice.