Hey everyone, could someone help me on this question:

1.
Evaluate the following using algebraic techniques, or show that they do not exist.

lim x--1^+ = sqroot(1-x^2)

Question

Hey everyone, could someone help me on this question:

1.
Evaluate the following using algebraic techniques, or show that they do not exist.

lim x->-1^+ =  sqroot(1-x^2)

anonymous · Answer

I'm just a bit confused on the + sign next to the -1

anonymous · Answer

That means the limit as x approaches -1 from the right

anonymous · Answer

Ahh i see.. so it doesn't really change the answer then? So i'll just plug in -1?

turingtest · Answer

You can't just plug in, we want to know what it approaches very close to but less-than -1

Plug in some values like -0.8 and -0.9 and see if it looks like we're going toward negative infinity, or positive, or whatever. 

That's what I figure they mean by "algebraic techniques", but I forgot the technical methods.

turingtest · Answer

oh sorry we're going from the right, so greater-than -1...

anonymous · Answer

I mean.... it depends on how rigorous you're trying to be, and what exactly you mean by evaluating a limit algebraically.  If a function is continuous, then the value of a limit at a point is equal to the value of the function at that point, so in that sense yeah, you can plug it in, but you should be aware that since this function is only continuous on the interval (-1,1) then that would not be valid approaching from the left.

anonymous · Answer

Oh i get it now, thanks for the help everyone. I appreciate it.

zarkon · Answer

the function is continuous on [-1,1]...for the same reason $$\sqrt{x}$$ is continuous on $$[0\infty)$$