given-fxfrac2-xx3216-find-lim-_x-rightarrow-6-fx

Name: given fxfrac2 xx3216 find lim _x rightarrow 6 fx
Uploaded: 2020-06-08
Duration: 1 min 3 s
Channel: Numerade
Description: Given $f(x)=\frac{2 x}{x^{3}+216},$ find $$\lim _{x \rightarrow-6} f(x)$$

Question

Given $f(x)=\frac{2 x}{x^{3}+216},$ find $$\lim _{x \rightarrow-6} f(x)$$

Elizabeth Xu · Accepted Answer

So here we&#x27;re looking to find the limit as X approaches negative six of f of X. We can stop a plugging in different numbers into our table values journey with numbers from the left hand side such as negative 6.1 negative 6.1 and negative 6.1 That means that our Kovacs is equal to 1.11 Could we get 11.11 in 1 11? Wait 11 So, as you can see from the left inside, our limit is going towards infinity. On the right hand side, we can plug in numbers such as negative 5.9 negative 5.99 negative 5.999 which gets us affects. We have 1.11 negative. 11.11 United have won 11.11 So here our limit is getting towards negative infinity. So that means because I left him. Limit does not equal the right hand limit. That means our limit when, except which is negative. Six of f of X does not exist

Elizabeth Xu · Answer

to find the living as extra purchase. Negative to vex will be. First thing to do is use our table of values to see if we left him limit in the right hand limit. Beat about a point. So are left element as X approaches native to from the left side you have a table. Values here will be completed. Different number, such as negative 2.1 night of 2.1 negative 2.1 So in excess equal to negative 2.1 f of X is you go to 34.41 Don&#x27;t get 304.0 floor, then we get 3004. So, as you can see here are Activex is increasing drastically, which means that our limit as X approaches negative to the left side is equal to infinity. No, On the other hand, if we were to locate it from the right side or punky and numbers such as negative 1.9 and negative 1.99 and negative 1.9 time So you have number such as 26 point negative. 26.39 negative 296.4 in negative 2996. So, as you can see here as Ex gets closer and closer to negative two f of X gets closer to negative infinity. So because I left him limit and a right hand limits are affinities. I wear regular limit, cause not exist.

Jade Meyer · Answer

So the question gives you that the limits of the function FX as execute your six equals four, and it asks you Khun, to compute three other limits based on that information. So for the first limit, we can use one of the basic limit laws that relates to powers and routes. So we can actually say that the limit of Ethel X squared as X approaches six is equal to he entire limits of f relax as X approaches. Six squared. So since we already know that the limit of FX&#x27;s As X approaches six equals four, we can see that this equals four squared, which equals sixteen. So that is our answer part A. Now also get part B. The question asked us to find the limit of one over a flex as X approaches. Six. We can use another basic limit rule for this so we can say that this is actually equal to the limit of one as X approaches six divided by you limit of FX as X approaches six the limit as X approaches six one will always be equal toe one because X is not part of the function. So no matter what X will be. It will always be one. And on the bottom we were given that value is for so for party. We get the value one and force. Finally, let&#x27;s look at heart to see. They ask us to find you limit of X times, the root of the function as X approaches. Six. So, in order to solve this, we can use the Products law, which states that this is equal to the limit of acts as X approaches six times the limit of root f of X or after next to the one half as X approaches. Six. Remember, roots actually are and exploit it. We can actually simplify this even further by using the law regarding powers and roots. So we can say that this is equal to the limit of Access X approaches six times square root of the limit of F necks as X approaches. Six. To evaluate this, we know that the limit of Access X approaches six is equal to six, and we also were given that the limit of FX&#x27;s That&#x27;s approaches six equals four so we can do six times root for which equals six times two, which is equal to twelve. And for that is our answer for part. See

Alan Mullenix · Answer

number 39. We&#x27;re looking at this one sided limit as X approaches negative three from the left numbers a little smaller than negative three. So we see here that this looks like something we would like to factor. So let&#x27;s factor that bottom. It factors exports three X minus two. So the bottom has a factor that cancels out the top. And we have a new function that we&#x27;re going to investigate the one sided limit of, and now it&#x27;s one over X minus two. So it&#x27;s something to point out here the original thing we started with and this new item here are the same function everywhere except for negative three. In the original function, there is a hole and negative three. In the new function, there isn&#x27;t a hole. We removed that removable disk continuity. But if we&#x27;re worried about the limit, we don&#x27;t care what happens at negative three. That&#x27;s what the limit is about. So these two functions are the same, accepted the place that we don&#x27;t even care about, so this is great. So Aiken instead work with this easier guy one over X minus two, and with this one, there&#x27;s no longer a problem. We&#x27;ve removed that hold that was causing an issue, and we can just plug in negative three straight away to evaluate the limit. So that&#x27;s negative. 1/5. This one sided limit is negative 1/5.

Amy Jiang · Answer

this is given that our limit as X approaches to over fallen function what that&#x27;s equal to negative aids. And now we&#x27;re asked if I&#x27;d this fallen limit to notice that we have our function f of X to the power of to over three and recall or limit Paula&#x27;s specifically are law number six, which is our power. We can rewrite this as you can pull in our limit. Okay? And I we know that this portion what article? Two negative h Do we have negative eight to the power of to over three. And what is equal to would I give just, um, the cube root of negative eight is negative. Two squared that gives us for

Paul Teng · Answer

Okay, So for this problem, to give you a function f of X equals who actually eighth, minus two extra street. And they want you to evaluate the limit as w approaches to off that part of the U minus two divided by W minus two. Now, you can go ahead, and so I&#x27;m the first really little dysfunction, and then plug these into this formula and try to pass it out. However, or you can also realize that this form of ah, this form this limit form is also an alternative way to stay the definite limit definition off the derivative. Right? Uh, limit deferent. We usually see it. As you know, f over Exel&#x27;s age minus f of X, all over age over eight. And the limit, of course. Uh, by in this case, we can. This is the alternative way of saying that the off trying derivative at the point to So this problem is actually asking you to solve for a double crime at the point, x w or X equals to two. So you&#x27;re asking you to solve for this and I&#x27;ll make it a lot easier. So if we first took the first derivative you&#x27;re a prime of X. Using a powerful will get the derivative of X E eight is eight x 227 and the derivative off made to X, suggesting it to and three the constant. So I just become zero. So this is our first derivative. Now you take our second derivatives for ask double prime of X. Then again, we have to use the power room. So where they bring down the seven and multiplied by eight. So we get 56 times Exodus six because seven, minus 16 and negative two is a constant, so that becomes zero. So we&#x27;re left with this as our after the prime as a function of X, so we can do now is pulling in two for X two, yet 56 times, 2 to 6 power. And this this equals two, 3584. That is your final answer

Problem

Given $g(x)=\frac{6 x^{2}-x-1}{2 x-1},$ find $$\l…

Problem 65 Hard Difficulty

Given $f(x)=\frac{2 x}{x^{3}+216},$ find $$\lim _{x \rightarrow-6} f(x)$$

Answer

$\left(\begin{array}{c}\text { dne } \\ -\infty\end{array}\right)$

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