Studying Mathematics Thread

[robvalue]

How about left-hand and right-hand limits:

Say, you have a function h(x) = sqrt(x). Since we're not dealing with imaginary numbers, the domain in this case would the set of all nonnegative numbers, so the least possible argument of the function would be 0.

What is the limit of h(x) as x approaches 0 from the right-hand side (the positive side)? Well, the function from the right to 0 is continuous and ends at the value of 0 at x = 0.

But what about the left-hand limit as x approaches 0 from the negative direction? Well, since we aren't dealing with negative x's in this case, then it seems the left-hand limit is undefined. Did I get this right? Or should I actually consider negative x's since they do lead to well-defined values (and, therefore, the limit would be 0 as well)? Or is the answer context-based?

Yes, this is what I meant by "from above" and "from below", that's the same as right hand and left hand limits. Yours is probably better terminology!

If a function is defined only for 0 upwards, then it seems to me you can't take a left hand limit at 0, because there are no values to consider.