evaluate-the-limit-assuming-that-lim-_x-rightarrow-4-fx3-and-lim-_x-rightarrow-4-gx1-lim-_x-righta-4

Question

Evaluate the limit assuming that $$\lim _{x \rightarrow-4} f(x)=3$$ and $$\lim _{x \rightarrow-4} g(x)=1$$

$$\lim _{x \rightarrow-4} \frac{f(x)+1}{3 g(x)-9}$$

Jade Meyer · Accepted Answer

So we&#x27;re given that the limit of FX as X approaches negative four equals three and the limit of G vex as X approaches negative four equals one were asked to find the limit of F of X plus one over three G of X minus nine as its approach is negative. For To do this, we can just apply the basic limit laws. First, we can apply the quotient law so we actually get the limit off after the ax plus one as ex approach is negative for and then divided by the denominator, which is the limit of three G vex minus nine as X approaches for then we can actually separate this further, using the some water and the constable to lock first. Listening to some law, you can separate this into the limit of Catholics as X approach is negative for plus the limit of one as X approaches negative for and then in the denominator, we can change this too. The limit of three g vex as ex approach is negative, for which, according to the constant multiple law, is the same as three times the limit of G of X as X approaches negative for minus the limit of nine as X approaches negative for so now all we have to do is plug in values. We know that the limit of FX as mass approaches negative four is three. So in the numerator we have three plus and we also know that the limit of one as X approaches any value will be one because ex is not in the function. So we have three plus one divided by we know that the limit of G vex as X approaches negative for is one because they were given that value. So we have three times one minus and the limit of constant is that constant. So we get nine that is equal to four over three minus nine, which is negative six. So we get negative 2/3 as our answer.

Jade Meyer · Answer

given that the limit of the function F Lexx as except culture&#x27;s negative for is equal to three were also given that the limit of Kiev X as X approaches negative for is equal to one and were asked to find the limit of two times Ethel necks plus three times she vex as X approaches negative for Well. To do this, we can use the basic limit laws. The first law we can use is the somewhat So we can actually separate this into the limit of two times f of X as X approaches negative for times Sorry. Plus the limit of three times g vex as X approaches negative for we can actually simplify this even further by using the constant multiple law So we can change this into two times the limit of Ethel Axe as ex approach is negative for plus and we do the same thing for this limit. So we get three times the limit of chief ex as X approaches negative for and now all we have to do is plug in values. We know that the limit of f of X as X approaches negative forces equals three, so we can change this to two times three and we know that the limit of G of X as X approaches negative four equals one. So we can change us two plus three times one. This equals six plus three, which equals nine. So nine is our answer.

Alex Johnson · Answer

in this problem, we have the information that the limit is X goes to negative. Four of f of X is equal the three and we have the limit as X goes to negative four g of X is equal the one we&#x27;re trying to calculate the limit as X goes to negative four of f of X multiplied by G of X and the product Law of limits tells us that this limit could be simplified into the limit is exposed negative four of aftereffects multiplied by the limit as X goes to negative four of G of x, and this will give us three times one, which is three.

Alex Johnson · Answer

for this problem. We have the initial information that the limit as X goes to negative four of f of X is three and the limit as X goes to negative four of G of X is equal. The one we&#x27;re trying to calculate the limit as X goes to negative four of G of X, divided by X squared and using the quotient wall of limits. This could be simplified into the limit as X goes to negative four g of X, divided by the limit as X goes to negative four of X squared. And this gives us a value numerator of one and the denominator we use substitution. It&#x27;s a negative four squared. Their final answer is one over 16.

Linh Vu · Answer

uh, I&#x27;m no function f thanks. When Excellent. You far. You could unite uncertainly Mironova PCI X when x energy far you go to 27. And the question is going to find a living under thanks to get you for on the f Thanks. Plus she thanks me venting my chilled him street banks using the limit Probably day we can win him the Kocian off the limit on the caution we can register ihsaa caution and building it You know, I expect you for thinking that you far I&#x27;m the time will be f x plus g x in the bottom have job times she thanks. And now the next time we can push the limit into every single term. Now, that&#x27;s where in the bottom. And now if we get the next time will be you go to limit on a function of x X get you for president Limit that she Thanks. Next, get you for dividing by remaining in the shoe. Thanks. Get you for temps. Could, uh, leave me under a tree. Thanks. An expert You far. So now for this one being equal to were given to go to NYU plus, but this one. Get any coaching legend, this everyone and dividing by this one example. Good to do because of the constant times on. Try this one. Here we get exactly into 2 27 So now we get going to 27 26. Name running by 54. So we have 2060 valiantly. 24. He go to two and a three, and this would be the answer for the question.

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

Can the Quotient Law be applied to evaluate $$\li…

Problem 30 Medium Difficulty

Evaluate the limit assuming that $$\lim _{x \rightarrow-4} f(x)=3$$ and $$\lim _{x \rightarrow-4} g(x)=1$$

$$\lim _{x \rightarrow-4} \frac{f(x)+1}{3 g(x)-9}$$

Answer

$-\frac{2}{3}$

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