Use the graph to find the following limits and function value lim f(x) X+1 lim f(x) X+1 c. lim f(x)d.f(1)WQ MCLCELMIL DciUI uuOuy104gi DUACSYuui LiidiloOA lim f(x) ...

Use the graph to estimate the limits and value of the function, or explain why the limits do not exist, (a) $\lim _{x \rightarrow 0^{-}} F(x)$ (b) $\lim _{x \rightarrow 0^{+}} F(x)$ (c) $\lim _{x \rightarrow 0} F(x)$ (d) $F(0)$

Give me a problem. We're going to consider um the graph given to us because we can't show the graph specifically. It's important that we understand how to evaluate these problems. So there's a couple different scenarios we can run into, we can run into the jump discontinuity like this. Um Mhm. Yeah. Yeah. Where we see that this in this case that the limit won't exist and therefore we but we do see that the actual function exists, we see the function exists at zero. We can also have a case where the limit doesn't exist and the function doesn't exist in zero either. Um So that's one scenario then we have the obvious scenario where um the limit does exist at zero when we just have this graph right here and obviously equals zero. So that's the case where the limit and the function exist at zero. And then we also have other cases where the limit and function exists but it may not be the exact same value. So we have to be careful because we know that while they're connected the limit value and the function value do not have to always agree with each other.

For the income we want to um consider the limit as X approaches for from the right. As X approaches negative 2013 and four from the left. So we're gonna just take a generic craft and analyze what that's gonna look like. So we're going to take X to the fourth. And again, there could be breaks in the graphic to be careful with this because that's how limits are going to change depending on if there's breaks in the graph. But in general, if we want to see the limit as X approaches and negative for then we see what's happening as we approach from the left and what's going to happen as we approach from the right, for example, And we see that we'll end up getting value about 16, which makes sense. We can also do the limit as x approaches and negative two From the left and the right. We end up getting what appears to be the value for. That's how we can evaluate these limits. zero would give us zero. But again, it's not always the simple. There could be breaks in the graph, and we have to make sure that the limit as we approach from the left is equal to the limit as we approach from the right in order for the full limit to actually exist.

Okay. Were asked by love. It's his ex approaches one left backs. Well, let's see where is negative Going nuts here, if you notice are left sided Limit. Use us one. And a right sided limit gives us They could do. Since they're not equal, this does not exist. Okay, We also have limit his ex approaches one of the Mex. Okay, What did not give me? Well, ones over here. If you approach from the left and the right, you get one of those limits equal to one. What's the limit? As extra coaches go right to the next over the approach from the right, get that secret to know. And then what? The limits as just you. Thanks. Well, if you see here, it's approaching from our left. And that's equal to one here. And I assume from the right as well it's approaching that value. So that's equal to

For the following problem we want to use the graph of F. And the figure defined the following values or state that they do not exist. Um So we first want to um say that F. of Wanna Scan equals zero and then um Since we have FA Fine Equal zero. We can't necessarily determine what's going to happen with the limit because what we see is that the limit as we approach from the left is going to be one, but the limit as we approach from the right is zero. So based on this, what we see is that um what we see based on this is that the limit itself is not going to exist even though the function actually exists. So we see the limit, it does not exist.