if-lim-_x-rightarrow-1-fracfx-8x-110-find-lim-_x-rightarrow-1-fx-2

Name: if lim _x rightarrow 1 fracfx 8x 110 find lim _x rightarrow 1 fx 2
Uploaded: 2020-05-28
Duration: 4 min 2 s
Channel: Numerade
Description: If $$\lim _{x \rightarrow 1} \frac{f(x)-8}{x-1}=10,$$ find $$\lim _{x \rightarrow 1} f(x)$$

Question

If $$\lim _{x \rightarrow 1} \frac{f(x)-8}{x-1}=10,$$ find $$\lim _{x \rightarrow 1} f(x)$$

Yaw Asomani · Accepted Answer

you have limits the limits. X approaches one of ffx minus eight Over, uh, experience one. We have this asked. 10 given, Right. Eso When is the limit? As X approaches one off ffx. Right. So what is the limit as executions one of FX. Okay, so? So we want to find this one. Ah, you know, this limit exists Limit except delicious one. Ah, for F of X minus eight. This one exists. And how do we weaken this dysfunction? Here is the same ass, right? In F off X minus eight over X minus one times X menstrual. This is the same as this, right? Because this is gonna cancel this one. Ultimately. And they gonna have this guy again, right? So nervous, saying I&#x27;m just rewritten in a differently street. Egypt. So you wait. Right? So this is the same thing now. We knew that we can separate those limits. This limited the same as limit. Except for which is one every thanks. Minus age over minus 8/1 and times limit. Except for X. A precious one of those who can split the limits. Right? We know that We know what this limit is. It has been given, right? That limit ISS 10. Right here. So? So here is gonna be 10. Mortified by the limit as X approaches one except wishes one except religious one of this. When you put one here, this is gonna be zero. Right? So this is you know, so, actually, the limits as X approaches one off F X minus eight has been shown to be zero. Right now we want a fine the limit of just FX. So how do we write it? No. In the middle of every face, everything X minus eight Ever fix can also be written as f off eggs minus eight plus eight. You can write it like that. Just sort of Samos after face. We&#x27;re using it because we have our results. Now we can use immediately. Right? So this one is also the same as the limit except which is one off every face minus eight, then plus the limit exit, which is one of eight. Right. The limit laws houses to do this. Now, what is this one where we found that that one is here, here. Simply said that within a zero. So this is gonna be zero and then. Plus, what is the limit? This limit? Well, this Let me Here is eight, right? Therefore, this limit the limit of this one is eight.

Daniel Jaimes · Answer

in this problem. Number fifty nine of this tour Calculus Ace Edition, section two point three If the limit is experts, is wonder of the function half of X, minus eight over X minus one is he quoted ten find The limit is expert is one of the function. So since we&#x27;re given this definitive statement that this woman is equal to ten all user limit laws to, ah rewrite this limit instead, as the Limited six pushes one of F minus the limited experts a sick one of eight Tiger Bhai and Element is ex purchase. One of the quantity x minus one crony calls attention. So we&#x27;ve used a limp laws that allow us to separate this quotient within the limit into a division of to limits and then the difference of limits in the top and the difference instead of a limit to the difference of limits at the top. And notice that this term here he said to me, one to solve for So let&#x27;s go ahead and do that. I want to write about Science Limited Express on the ref minus Tell a man his ex precious one of eight. It&#x27;s equal to ten times&#x27;s limit his expressions wanted. Explain this one. We can you know the other element to the right hand side. So on the left and saying we have limited express is one of F equals ten times limit and exporters one that it quantity experience one a month element x x perches wanted Great. Now its exports has won This quantity explain. It&#x27;s one is equal to one minus one or a zero and in time zero zero. So end of kidding is that the limit, as an expression of wonder, is equal to zero plus is limited. The limit is export. Just want to eat a being in a constant value. Therefore telling it is equal to eight. And this is our final answer as to what the limit is. Export is one of the office.

Carter Rogers · Answer

the information provided to us in this problem is that the limit as experts is one of f of X is eight limit as experts one of g of X is three and limit as X approaches. One of h of X is too and we&#x27;re being asked to evaluate the limit as experts. Is one of f of X, divided by H of X to the limit law that&#x27;s going to help us here is that this evaluates to the limit as X approaches one of f of X divided by the limit as X approaches one of h of x oops and we were given this information in the problem. So the limit as experts is one of FX. It&#x27;s eight sweet employees that in in the numerator and on the bottom, we have limit as experts is one of age of X, which we know is too, and eight divided by two gives us for

Christopher Ying · Answer

we are asked to find the limit as X approaches. One of effort backs over the quantity g of X minus H of X and were also given the values for the individual minutes over here. So using this information, how are we able to solve for this, uh, much larger expression? Well, the first thing that we need to do is we need to employ our limit law of Division, and I&#x27;ll give you a quick run down and where is limited as X approaches A of FX over some G of X will equal the, uh, the division between the two individual of limits. What I mean by that is the limit of f of X over the limit as X approaches a off G of x. Great. So, knowing this information, let&#x27;s apply it to this problem right here. Well, first, pretty much I couldn&#x27;t do it verbatim. Hold on. Let me just box this really quickly. Make sure you guys have this highlighter in your notes. Super, super important. All right, so let&#x27;s let&#x27;s let&#x27;s apply with long division to this one. So what happens is will take the limit of both top and bottom, so it becomes the limit as X approaches one off FX. Well, divine that by the limit as X approaches one of G attacks Linus H of X. Great. Let&#x27;s first all from the bottom because it seems a little bit more difficult. We already know what the top is. We&#x27;re just gonna have to play an eight later so we can hold off on doing that. Let&#x27;s first all from the bottom. So all right, the bottom two side here, let&#x27;s say limits. As acts approaches one of G of X minus h of X on a solve. This expression will need to employ another one of our limit losses live in los subtraction. Remind you what that is. All write it down for you. Limit as X approaches A of, uh oh, wow. We could use gox, but I&#x27;d rather use f of X cause I like Catholics and looks nicer. If that&#x27;s minus g of X, we can, uh, broke this apart into the difference of the individual of this meaning X minus a X. There&#x27;s our X to a FX minus that you limit X X approaches a g of X, applying this to original expression that we want to solve for Get the MIT expert. Just one dnx minus the limit as X approaches one, uh, h of X. Great. We actually know what these two values are from Are given. We know that G of X is going to be three and h of x gonna be you, the two. So this simply becomes three. Minus two staples. One Great. So we know that the denominator is going to equal one here. We also know the numerator is going to be equal to eight. So let&#x27;s plug all this information in will often get eight over. That&#x27;s a big divisions and look over one. She pulls eight great saw. They&#x27;re old.

Carter Rogers · Answer

So for this question, were given the information that the limit as exit purchase one of some function f of X is equal before. And then we&#x27;re being asked to evaluate that limit as X approaches. Negative one of f of X squared. We&#x27;ll go ahead and plug in that value of negative one so f of negative. One squared now negative one squared. We know that that&#x27;s just one. Some were given F one, and we know f of one from over here is four. Because the limit as X approaches one of f of X is for so we know that this is just for

Amy Jiang · Answer

okay So far apart. They were asked to find a limit. As X approaches we get to about the Mets. You know, Sadd&#x27;s we only asked to find this portion here. So it&#x27;s all our equation for the limit ads. So let&#x27;s start by using our Kocian girl so we can squid a parliament into two minutes. Okay? And now we know that this limit that&#x27;s equal to two negative two squared, which is for multiplying by four on both sides we get our limit is equal to four now for part B, we want to find the limits as X approaches Negative two of FX over X. So what we can do to our equation here is we could multiply both sides by X and we would get the limit as X approaches native to of aspects Homer and the limits using our Kocian role of negative two over X is equal to ex itself. We would also need a limit here. Okay, so that would give me this whole limit is negative two. And this one is going to actually we want to keep this limit here since we want f of X over X. So this limerick here is going to So we see that our limit is even too negative too

Problem

Prove that if $\lim _{x \rightarrow a} g(x)=0$ an…

Problem 61 Hard Difficulty

If $$\lim _{x \rightarrow 1} \frac{f(x)-8}{x-1}=10,$$ find $$\lim _{x \rightarrow 1} f(x)$$

Answer

8

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