 So let's take a closer look at continuous functions. So we might take a look at the type of information you might get from a flight data recorder. And so here we have an airplane traveling from New York City to Los Angeles, both of which are at sea level. And we might record information about the altitude of the plane in kilometers above sea level, t hours after takeoff. Unfortunately, the plane flew over a top secret installation and the government erased the data to conceal the existence of a common software glitch that caused the data to be erased. T1. So we don't have a record of what actually happened between hours 2 and 3. But the truth is out there, and you can't hide it, so let's find the limit as t approaches 2 from above of h of t. Since this is the graph of y equals h of t, we can find the limit as t approaches 2 from above of h of t by finding the values of y as t gets close to 2 from the right. Except we don't have that part of the graph. So what can we do? Well, one thing we might do to proceed, let's start with something that we do now. We can approach t equals 2 from the left, and so this suggests that we know the limit as t approaches 2 from the left of h of t. Since we can approach 2 from the left, we know the limit as t gets close to 2 from the left of h of t is going to be 8. Now we don't know whether this is useful, but it is a fact, and so let's go ahead and record it anyway. What else do we know? Well, one useful thing to remember is that the unqualified limit exists if and only if the one-sided limits exist and they agree. And so we also know that if the unqualified limit as t approaches 2 of h of t exists, then the limit as t approaches 2 from below and the limit as t approaches 2 from above and the limit as t approaches 2, no plus, no minus, all have to be equal. And so we have to ask ourselves, self, does the unqualified limit exist? Well, one way the existence of the unqualified limit would be guaranteed is if h of t were continuous. And that's because one of the requirements for a function to be continuous is that the limits must exist. So if we'd like our function to be continuous, we might ask ourselves what would make it be discontinuous? As we saw, there are two situations where a discontinuity occurs. A discontinuity occurs when the function isn't defined, but the plane always has some altitude, so h of t is always defined, so this case can't apply. The other possibility is the function has a break, but this would require that the altitude change instantly from one height to another, and that's physically impossible. So this situation can't apply either. And what that means is that h of t must be a continuous function. Since h of t is continuous, we know that the limit as t approaches 2 of h of t exists. But if the limit exists, then the limit has to be the same whether we approach it from the left or the right. And that means that the limit as t approaches 2 from above and the limit as t approaches 2 from below have to be the same, and we know this limit as t approaches 2 from below. And so we know that this limit is going to be 8.