use-a-graphing-utility-to-a-graph-the-function-and-b-find-the-required-limit-if-it-exists-lim-_x-r-3

Question

Use a graphing utility to (a) graph the function and (b) find the required limit (if it exists).
$$\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}+5 x+2}-x\right)$$

Darshan Maheshwari · Accepted Answer

All right, so the graph is over to the right off. Question 65 on. We have to find a limit as extending towards infinity. So basically, we need to find, uh, when this exists and in towards infinity. So we already see that we have ah, horizontal as, um told at 2.5. Yeah, So as extends to infinity, the graph approaches this 2.5. Since this over here, we have three. So this must be 2.5. So the limit for this is 2.5 or fireworks.

Darshan Maheshwari · Answer

so in question About 66 the graph is over to the right of the function we need to find the limiters extends to infinity. So we can clearly see that the X axis is actually, uh, a Nazem told. So when extends to infinity, the graph off the graph tends touch the X axis, which means that the value of the functional value approaches to zero. So the answer for the limited zero

Darshan Maheshwari · Answer

question 64. So the graph is over to the right that is off signing trees to the products on towards the right side of zero, which is over here we have to find the limits of this value is 0.84 months. So the limit value consort as your appointed for one, which is her concert.

Julian Wong · Answer

problem. We&#x27;re being asked to evaluate the limit his ex to infinity of Ah, this expression here and ah, recall that if we&#x27;re valuing a limit to infinity, we don&#x27;t actually care about every single term. We only care about the highest degree term. So when we tried to expand the top, it&#x27;s gonna be a little bit messy. But notice that we don&#x27;t actually care what all those terms turn into. We only want to care about the highest degree one which is applying the Cube to the highest degree term currently, which is the two x to the power five or three. That would give us eight X to the power of five all over X to the power of five. So, uh, we would divide all the terms by extra power five. Since that&#x27;s the highest degree in the denominator. So we&#x27;ll have thes doctor detected dots over extra five plus eight x of the five over X of the five over next to the five over X to the five and ah, all these lower degree terms that we didn&#x27;t care about, they would tend to zero, so we don&#x27;t care. And that means we&#x27;re left with limit as X goes to infinity of eight over one, and that&#x27;s just equal to eight

Linh Vu · Answer

but I use on my coverage. Accurate. So I need to scan the graph on fishing now. Yeah, you have. We have one plus the five X power off the 1/3. And Dan, you have plus two X power off five. Number three, and then we have totally power off. Uh, the big power of the three here. And Dan, we derived by No X. Power five That extra incentive from the off. So it&#x27;s a very way. 53 Innogy knew his name. It here first step will be He signed that tree and dissected booth five hours into the experiment off, huh? Yeah, when they took under fire three. I should have this long will be image again. Find three X so b e o ah three minus Father three here and you just off. Now, do you have any expel five on the next Them? I would like to get about three inside, so it&#x27;s gonna get off scythe. No, 543 Just way. Have the about tree back five. Now we can cancer expert fucking five and now has excellent June 60 freeholders in this way. Have exactly did you get

Linh Vu · Answer

here. Did you do the But I use on my girlfriend Gecker conduct this mosque? Yeah. I don&#x27;t grafted the craft A function here and the question asking that you find our limit on the function when x get u minus infinity. So going to see when extra Germans infinity the aircraft Affection and gratitude of off uh, we see that green handy got u minus idea. So you know what? You very find out what? I can do it by hand. Now I want to find a limit on the function under one plus five. Thanks para one of a tree. Ah, bless Teoh Angst verify on a dream. Totally about three. You&#x27;ve only been expelled. Five. So the first step we need to two will be on the top inside about three reflected an expert find victory. I was signed. Since then, we have the wonder money. But Expo 503 and bless five What is amusing? Get one other expo for under three because find of dreamers front treated You wanted a three and now plus two defending banks About five Now the next time I would like to do the three him to this on this one and they&#x27;re flying again. Done. Bring it. Thanks. Just humans. Infinity fun is when they get X about five and funders when we should come being again Just 51 number expert for under three plus two about three by five. Now here we can see what can comes Another ex verified and s x g infinity. You see, This one goes to zero. Isn&#x27;t on some good genes? There are. And then we have any left would, uh, geo tree and do about two equals to eight. So it doesn&#x27;t matter with the one we found in the graph of the function here. So you could you it could you? I&#x27;d Here is a limit and the function when Xkj minus infinity.

Problem

Use a graphing utility to (a) graph the function …

Problem 65 Easy Difficulty

Use a graphing utility to (a) graph the function and (b) find the required limit (if it exists).
$$\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}+5 x+2}-x\right)$$

Answer

$\frac{5}{2}$

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