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Let $\lim _{x \rightarrow 4} f(x)=9$ and $\lim _{x \rightarrow 4} g(x)=27 .$ Use the limit rules to find each limit.$$\lim _{x \rightarrow 4}[1+f(x)]^{2}$$

$$\lim _{x \rightarrow 4}[1+f(x)]^{2}=100$$

Calculus 1 / AB

Chapter 3

The Derivative

Section 1

Limits

Derivatives

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Okay, um, this problem to we're just gonna shift around the limit at lot of it so that we can find of the actual while you remember that were given the limit affects this X approaches for So what I will do here as I'm going to move that to outside of the limit using I believe that's well number six on your tax book. Okay, so, um, this will be limit of one class if a bags excellent approaches for amed come. We're moving the square outside of the limit, okay? And then, uh, let's also spread out the limit for what we have inside here. Notice that we can move. This is the same as saying limit of one class limit of effort. Texas Tech support floor. Okay, so let's do that. It will be next searching for for one class limit of backs. So I'm just teasing another one of their rules. That's given in your book. Page one sixty. Okay, X approaches for and then finally we have the square. Great. Now we know a limit of one which is a constant limit of the constant is just going to be It's always going to be the number, the constant itself. So here we have one and then limit of ever bags spent a fortune for as giving nine. So what we're doing is just one plus nine and then square it, so that would be a hundred. Great. That's it. So just to recap up first, I just moved the square. And then once I do that, I just spread out the limit into each function. One is just a constant, and then EPA backs on were given the value, and then it's just a simple Artem Itics after that.

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