## Intuitive Notion of the Limit - One-Sided Limits

HELP
 `f(x)` = `f(x)` = Examples 1. Jump discontinuities 1 2. Jump discontinuities 2 3. Continuous 4. One jump 5. Hole at x = 1 6. Exploding 1 7. Exploding 2 8. Infinitely wiggly 9. Shifted square root
We see here the function `f` graphed in the `xy`-plane. You can move the blue point on the `x`-axis and you can change `delta`, the length of an interval with one end at that point. The point has `x`-value `c`, and you can see the values of `c` and `f(c)`. You can type in your own functions in the left input box, or you can use the pre-loaded examples in the right drop down box.
We say `lim_(x->c+) f(x)` exists if all the values of `f(x)` are "really close" to some number whenever `x > c` and `x` is "really close" to `c`.

We say `lim_(x->c-) f(x)` exists if all the values of `f(x)` are "really close" some number whenever `x < c` and `x` is "really close" to `c`.

#### Explore

1. Often, a one-sided limit exists even if a (two-sided) limit does not exist. Which examples have points where this is the case?
2. Can you think of a situation where a one-sided limit doesn't even exist? Example 8 shows such a situation.
3. Consider Example 9, a shifted square root. Does the left-hand limit exist at `x = 1.5`? What about the right-hand limit? The normal (two-sided) limit?
4. Is it possible for a limit to exist, but one of the one-sided limits does not exist? Is it possible for a limit to exist, but neither of the one-sided limits exists?