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Question

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

Helen Telila · Accepted Answer

Okay, um, this problem to we&#x27;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&#x27;m going to move that to outside of the limit using I believe that&#x27;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&#x27;re moving the square outside of the limit, okay? And then, uh, let&#x27;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&#x27;s do that. It will be next searching for for one class limit of backs. So I&#x27;m just teasing another one of their rules. That&#x27;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&#x27;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&#x27;re doing is just one plus nine and then square it, so that would be a hundred. Great. That&#x27;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&#x27;s just a simple Artem Itics after that.

Julian Wong · Answer

you&#x27;re trying to find the limit as X goes to four of two to the F of X and one of the limit Law says that we can just apply the limit to F of X service is two to the power of limit as X goes to four of f of x and ah limit as X goes to four. Buff of X is given to us. That was nine sub two to the power of nine, which gives US 512.

Linh Vu · Answer

I have no function f x when x great you for in court tonight and it wasn&#x27;t asked to find a limit on the June member of the function f X and X years too far a condom use in the limit property. We can push this limit. Yeah, passing through the exponential function The information have that you are under limit on the function f x x get you far And now this one is given to us Go to tonight if you have a job out night and Juba And I would include you too far 500 on trial for him and that will be the answer.

Julian Wong · Answer

okay. The limit as X goes to four of F of X plus g of X, all over two times g of X here and our limit Law says that we can apply that limit as X goes to four to each function, so limit as excuse to four of F of X, plus the limit as X goes to four of G of X all over. The constant multiple is pulled out two times and limit as ex ghost of four of g of X and ah, we know what those limits are. It&#x27;s given in the question. It&#x27;s nine plus 27 over two times 27 so that will give us 36 over 54 that&#x27;ll reduce to to over three.

Todd Vawdrey · Answer

okay. In this problem, we&#x27;re given that the limit of some functions experts is four is of F of X is nine and the limiters experts for G of X is 27. We don&#x27;t know anything else about the function accepted that the limit exists and we need to find the limit of the function f of X minus G of X so we can apply our limit rule and limits will distribute over addition and subtraction. So we&#x27;re looking for the limit as X approaches for of f of X minus the limit as X approaches for of G of X and we can just do a substitution in there. This is the number nine minus 27 so altogether comes out as a limit of negative 18.

Linh Vu · Answer

I wasn&#x27;t even though early it from the function. Have expert expert you for you could unite and a limit on the function G exponent x that you for the coach Gender seven. And it wasn&#x27;t asked her to fight darling on the FX minus she x When x rays too far by their limited rose him, we can displayed a limit into it up them if we have the limit on the function f x minus limit for X when both thanks gets you far for both case nears. And for this when we get equal Jew nine and fathers when we get equal Joe 27. And if when we get to go ju minus 18 and don&#x27;t give me the answer.

Problem

Let $\lim _{x \rightarrow 4} f(x)=9$ and $\lim _{…

Problem 28 Easy Difficulty

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

Answer

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

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

Calculus with Applications

Anna Marie V.

Caleb E.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Margaret L. Lial • Raymond N. Greenwell • Nathan P. RitcheyCalculus with Applications

Anna Marie V.

Caleb E.

Michael J.

Joseph L.

Margaret L. Lial • Raymond N. Greenwell • Nathan P. Ritchey

Calculus with Applications