if-4-x-9-leqslant-fx-leqslant-x2-4-x7-for-x-geqslant-0-find-lim-_x-rightarrow-4-fx-4

Name: if 4 x 9 leqslant fx leqslant x2 4 x7 for x geqslant 0 find lim _x rightarrow 4 fx 4
Uploaded: 2020-05-27
Duration: 1 min 36 s
Channel: Numerade
Description: If $4 x-9 \leqslant f(x) \leqslant x^{2}-4 x+7$ for $x \geqslant 0,$ find $$\lim _{x \rightarrow 4} f(x)$$

Question

If $4 x-9 \leqslant f(x) \leqslant x^{2}-4 x+7$ for $x \geqslant 0,$ find $$\lim _{x \rightarrow 4} f(x)$$

Yaw Asomani · Accepted Answer

Okay, so we have the limits of, uh, this inequality, right. This is Geo. Thanks. Uh, this is you, FX less than or equal. Teoh, uh, exited four minus exit of four, minus X squared. Right. And then close to right. So you want to find a limit as X approaches? Um, one right as execution. So you can see that this function here is sandwiched in between these two functions, right? In fact, the squeeze Dearen can also be called as the sandwich rule. Right? It is when you hear a squeeze serum is the same as the sandwich rule. Right, Because this is sandwich in between these two, uh, functions. Right? So you think the limit as X approaches one off the 1st 1 that is two times one right, which is just you. And then we take the limits as exit, which is one of the 2nd 1 right? It&#x27;s just gonna be off the this one. Is this gonna be once in a four minus one squared, right? Then plus two, Which is also to write so by the squeeze theorem ordered by the sandwich Who any of them is the same thing by the same each rule. You can see that, uh, the limit as X approaches one of the effects. It&#x27;s also too

Yaw Asomani · Answer

So you want to do, um four X minus nine. Less than or equal Teoh Every thanks lesson. Or he could you, um ex weird minus four X plus seven eight eso. I want to find the limits as X approaches four off FX, right? So we can see that every next year would not know exactly what it is. But what we know, the information we have is that it is sandwiched in between these two functions, right? So what it comes into mind, you guessed it squeezed the room. So we take the limits as X approaches for off the left hand side of the function. Uh, this is just gonna put four there. So this is what you have. Eso This is 16 minus nine, which at seven. And then you take the limit as executions for off the right hand side. Also another function. So this adjustment before squared, right minus for then plus seven others when it zero. So it is just seven left here, right? So this one is also seven. So the limits as X approaches for the left hand side is seven. The limits, as executions for right hand side is also seven. Therefore, we are permitted to use the squeeze theory. So the limits the limit as X approaches four of ever affects. It&#x27;s also seven by the squeeze.

Daniel Jaimes · Answer

this problem. Number thirty seven of the Stuart Calculus, It&#x27;s edition section two point three, if for X minus sign is less than or equal to FX, which is a sin equal to X squared minus. For experts, seven. Poor X is greater than equal to zero. Find the limit his expertise for of F. So, given this information, we can attempt to find this limit. Ha ha! By use of this quiz here and possibly let&#x27;s applying this limit to each of the functions this part is for for expand its time. Last ten limited his expertise for Andre unless they&#x27;re equal to the limited experience for of X Squared minus for X plus seven. So here, if we apply thanks, is expertise for and we figure out the limit for the lower function on the upper function, we should be able to make ah, a announcement of what this limit should be. His expertise for for X minus nine approaches four times four or four squared minus nine and his ex approaches for for the upper function X squared minus four X plus seven Purchase four squared minus four squared for seven. Here we have sixteen minutes time which is seven. And for the upper function we also have sixteen minus sixteen plus seven, sixteen, sixteen zero. So we just have seven for that function. And because this limit has to be great for them or equal to seven and listen or equal to seven, we can definitely state that the limit X approaches for and then right the squeeze, dearie must equal seven.

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.

Helen Telila · 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.

Problem

Prove that $$\lim _{x \rightarrow 0} x^{4} \cos \…

Problem 34 Easy Difficulty

If $4 x-9 \leqslant f(x) \leqslant x^{2}-4 x+7$ for $x \geqslant 0,$ find $$\lim _{x \rightarrow 4} f(x)$$

Answer

2

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Catherine R.

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Samuel H.

James Stewart

Essential Calculus Early Transcendentals