Limit of Multivariable Function: Does it Exist Despite Undefined Simplification?

[chetzread]

Homework Statement

Is it true that e find that the function is undefined and we can't simplify them, then the limit of multivariable function is surely doesn't exist

http://imgur.com/a/cihXu

Homework Equations

The Attempt at a Solution

Is it possible that we already try many different of y = x^n , n is all real number , the limit still the same ? ( the limit of function actually not exist , but in our working we have tried many different of y = x^n , n is all real number , we keep on getting the limit of the graph still the same ) ?[/B]

 

[BvU]

HI,
What is it you are asking ? Limits of $f(x,y)$ are a different matter than limits of $y = f(x)$ !

 

[chetzread]

yes

HI,
What is it you are asking ? Limits of $f(x,y)$ are a different matter than limits of $y = f(x)$ !

yes , i am asking a limit of f(x,y)

 

[BvU]

So why write $y=x^n$ ?

 

[chetzread]

So why write $y=x^n$ ?

in 3rd attempt , the author want us to try substuiting different value of curves / lines into the function... so i use y = x^n

 

[BvU]

Did you forget to tell us what function it is you are investigating ? And what limit at what point (a,b) ?

 

[chetzread]

Did you forget to tell us what function it is you are investigating ? And what limit at what point (a,b) ?

I am asking generally, the function could be any function of x and h, and the limit could be anything...