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. (10 points) Use linear approximation to estimate e −0.004cos((−0.004)(0.09))9. (10 points) Identify the region described by the inequality x2 + y 2 + ...

Question

. (10 points) Use linear approximation to estimate e −0.004cos((−0.004)(0.09))9. (10 points) Identify the region described by the inequality x2 + y 2 + 2z 2 > −4

. (10 points) Use linear approximation to estimate e −0.004 cos((−0.004)(0.09)) 9. (10 points) Identify the region described by the inequality x 2 + y 2 + 2z 2 > −4



Answers

Draw a hand sketch of the inequality. State the boundary of the region.
$x^{2}+y^{2}<9$

We need to do. Is it? Did you find an excellent ascent? And now I should have the language is zero. It means then that's good. Thanks. Plus x square in coach's. Oh, and because you means that on it cannot be coaching because it isn't principio, mister, I'm supposed to. And the only way I can Coach is on if if executed, you so endzone in interval off. Ah one and I therefore I can compute exact area. And now so are you, uh, go Joe into girl from one tonight And then we have, uh It's good that Thanks Bless. Thanks. Square X on Now we will have untied review under one of ah Scott of Mexico, but you expel in tree. I wanted to dividing by three times. Two plus thanks for Jeeva. Victory Evil right under one and night. And you're not nickel a Jew? Uh, 203 9 Power 32 plus Nyberg tree over three, minus the two out of three. Plus one of the three. So here we go on the joint a three night. Could you three square So three square and we have a balanced. And up to this they were going toe. Aah! Night about nine. About three. Know about good. You 7 29 in mind by three. Goes to 2 43 and then minus is when they go to one. And now we can't go. Joe jokers another joint and we have a tree. And about three got around that you have a nine, madam. Still be 18 plus through 43. Could you 2 16 1? I have two minus column here. So it would be to 60 here. Supplied Johnson will be minus one hand. They could do six.

So for this problem, we want to start by finding T Samton. I'm in. In order to do that, we're going to need to find our left and right hand reading sums with 10 7 Devils. So we know that our Delta X is going to be equal to a B minus A So nine minutes, one over a number of seven novels, which is 10. I'm so this will just be eight over 10 and we know that for right hand Roman sums ex of i star is going to be a which is one plus Delta X I so eight I overton, um, and for a left hand room in some except I start, it's going to be a plus eight over 10. Um, but this time times I'm minus one. And so from here we have all the information that we need to calculate our Robinson's. I'm So, for instance, are 10 is going to be dealt X, which is eight over 10 time signal going from eyes one up through a number of steps, just 10 of f of x abi star. So the square root of one plus eight i over 10 plus one plus eight I over 10 squirt. And will we evaluate this? We get our 10 is going to be equal. Uh, 2 293.64 And in order to evaluate l sub 10 were essentially just going to do the same thing. Um, crap Plug in eight times I'm minus one over 10 of into our exit by formula. And when we do that, we get Elsa 10 is equal to 228.4 So when we average these but adding them together and then dividing we are going to get that tea. Some 10 is equal to 260.84 And so our last up in this problem is calculating our actual interval using the fundamental beer with calculus Part two. So this is going to be equal to the integral from 1 to 9 of the skirt of X, which I'm going to rewrite as Ex The 1/2 power plus X squared DX and the reason that I rewrote a squirt of X as X the 1/2 power is in order to make it a little bit easier to use are powerful Once we know that in order to take the interval here, we're going to do one over this. Excellent plus one. So one over three house times exit 3/2 hour plus one over this echo nit one. So 1/3 x cubed. And this is only going to be violated from 1 to 9. So essentially, what we're going to do is have 2/3 will be taking the reciprocal veggie nominator times nine to the three house power close 1/3 times nine kids. And then we're going to subtract a same thing, but plugging in one so 2/3 times one 23 hours power plus 1/3 time's one cube and only simplify. We find that our actual integral is going to be equal to 260 which we can see is only an error of 0.84 from our original T said 10

Hello. Do our duty A good person? Our problem. The 51 from the section will transmit replay here we have minimized the square of the distance. The guarantees there because in the square last guy quit and it points up lungs. It was little so therefore excellent gang better done us x minus like the hosts Claire. But Life choir plus they're square. Do you explains there can be X square plus life. Where mine is that Because Phil So they're tired because Lamba in tow, we get built f as their dive because Rupinder X minus learned not truly gone out Cool. They're g equals Lex Gola Gola Mine A slur So that in the X minus one equals extra lambda. Similarly cool. It was to my lambda bruise that income minus Lunda. Now the best part comes here. If my is not equals zero, then Atlanta will be going to work. The plastic creation is inconsistent. If one equals funeral, it can strain. Gilles is they eat books. Thank you. Where and comparing the first and the third equation. Your vote is for you. Blessed to Lex minus two. It will fill. So Richie knew manganese ore refined about its equals. There's little point fire a night. And by equal zero Is it because little 0.3478 thank you.

So we're given to functions here and were asked to found the bounded region. So um we're going to be sketching that region, We're gonna be approximating the area of that, setting up the integral and then finally calculating the area of that bounded region. Okay, so the first thing to do is to sketch are two functions that are given. So the first function X squared minus nine is a little bit nicer to sketch. It's just a nice um quadratic but it's been shifted downward. The next function is also a quadratic, It's in a factor form. Um we do know it's pointing upward because we can see that positive X squared um with the two in front, that just means it's a little taller and skinnier. Okay, so let's go ahead though and find it zero so that we can um plot it a little bit easier. So I'll put that to X -1, equal to zero by adding the one and then dividing by the two. I get a zero of a half and then the other one I can see my zero is negative three. Now in order to sketch this um I'd like a little bit more information right now. I know that that second quadratic is going to be skinnier. I'm just not quite sure of where it's going to um intersect with the first one I drew. So I'm gonna find my points of intersection. So just know you don't always necessarily do all the parts in order. It just you want to gather information whenever you can. Okay so in order to find our intersections, I put the two functions equal to each other and I'm gonna be moving everything to the same side because it is a quadratic. That means we need to factor in order to solve it. So I did subtract an X squared and add nine to both sides. Okay so now I can see since he's multiply to six beneath to add to five, the best thing to use would be a two and a three. So now if I set those equal to zero, I see that X equals negative two and X equals negative three. Are my intersections. This is going to allow for me to more easily draw that quadratic. Now if I really really zoomed in um I would see that the X squared minus nine is on top. I also know that um because if you see their coefficient, that's a coefficient of one where my other function has a coefficient of two which means it's taller and skinnier. So that's the only way that they're if they're going to intersect at those two places, how that could happen. So I'm gonna go ahead and write my inner girl. I'm integrating from negative 32 negative two. And my top function is that X squared minus nine. And then also track the bottom function now. Um To actually subtract this we can again just look at like terms but we've actually already subtracted one a function from another when we got that X squared plus five X plus six. So instead um though we're starting with the X squared minus nine and we're subtracting the other function. So we're just gonna get the opposite signs. So we'll have a negative X squared minus five X minus six kate. Now we're ready for our power rule so we'll be going up a power reciprocal. So here we have um one third in front with our X. Squared. We'll also have that divide by two. So I'll write that as five halves And then we have -6. We're gonna be placing our negative two in first and then we'll subtract placing the negative three in. So if we put a negative two in now do note when you take something to the third power and it's negative and negative will come out of that. So are two negatives cancel with that first term. And then we can place a -3 in. Now. We just need some common denominators and um to actually find the solution here It equals 1 6.


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