Limit of Function at (-1,3): Does it Exist?

[Nope]

Homework Statement

http://img23.imageshack.us/img23/9366/95631341.jpg

Homework Equations

The Attempt at a Solution

If the dot (-1,3) is gone, does the limit of x->-1 exist??

 

[Dick]

How do you conclude lim x->(-1)+ is 3? And why do you think lim x->(-1) doesn't exist?

 

[physicsman2]

Yeah, you should check E and F
you got f wrong because e is wrong
for e, why did you say that the answer is 3
if the question was f(-1) = ?, then the answer would be 3

 

[Nope]

no.., just ignore the answer
I know x->(-1)+ is 1
but is x->(-1) exist ,if the dot is gone?

 

[HallsofIvy]

Yes. The limit as x goes to a from below or above, or the limit as x goes to a, all depend only on the values of f(x) for x close to a, not at a. The value of f(a) is irrelevant to [/math]\lim_{x\to a} f(x)[/math] which may exist even if f(a) does not exist.