
Norm Limits
I hope this is in the right place, it feels like calculus, but it's the last part of my analysis problem.
Construct an example where g: R2>R lim x>a g(x) exists but lim x>a g(x) does not exist
I'm having a very hard time coming up with something to put this together. I think this is my theory behind it, does anyone have any ideas on something that would work?
Specify a continuous functiong(x ⃗ )= g(x,y) on R^2, which is not constant, and which cannot be strictly written as a function of r = √(x^2+y^2 ). Then, the limit of g(x ⃗ ) as x ⃗ approaches a ⃗,a constant vector,will exist (and will equal g(a ⃗ ) ), but the limit of g(x ⃗ ) as x ⃗ approaches a ⃗  (a constant positive number) will not exist because x ⃗ can approach many different values in R2 (and still havex ⃗ approach a ⃗ ), but the values that g(x ⃗ ) approach will be different.

Re: Norm Limits
Hey renelovexoxo.
This kind of question reminds of results in complex analysis where only functions that have derivatives are analytic. You might want to get an example of a complex function in C that has no analytic derivative and use that to get one for your example.

Re: Norm Limits
I think what you said is correct.
In the first limit, x is approaching some point, but in the second, x is approaching the circle x=a. So (assuming a is not the origin) it seems like any function that actually varies as you go around the circle would work.
 Hollywood