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KVY =Ax{P)Elnd new estlmates using ten rectangles In each case: (Round your nswers to one decimal place ) (lower estimate) (upper estrate)...

Question

KVY =Ax{P)Elnd new estlmates using ten rectangles In each case: (Round your nswers to one decimal place ) (lower estimate) (upper estrate)

KV Y =Ax {P)Elnd new estlmates using ten rectangles In each case: (Round your nswers to one decimal place ) (lower estimate) (upper estrate)



Answers

Estimate each sum by rounding the addends to the nearest ten. $$424.08+169.04$$

So this problem Ask us to estimate the integral off F by using the rectangle message. And if you have the tax, poke it and figure out that function F s a decreasing function. That means for for upper estimate you want to use so that one point because you know the function is decreasing, so the left point will be higher than the right point and similarities. If you want to use a lower estimate, they will have to be the Ryan Point. And once you figure this hours, it's just left to right down the end point off off its track tangos and the pace of its share of tangos. So so for proud, eh? If you want to use our five tangos, there's a chair of tunnel have based, too. And for the upper estimate? No. And it will be, Ah, the base of the structure knows, too a musical by some of height, in this case along to use the left hand points. So it's from fo zero. Remember, Ich Weiss based two's on the next one should be F off, too, and similarly for four I have six half off eight and the lower estimate we'LL have to use the right end point so you appear again faces too and height will be from F off too. And similarly, each one you increase. It's argument by two. So I'll skip the details. The last one should be half of ten and you can figure out the value ofthe the function by looking at the graph on your textbook and so for party. Similarly, the opera estimate it struck tango in this case because used ten off them and the lances ten. I will have the last one and you use the left hand points F zero us if one plus up to F off nine, which is a laugh of m point of the last rectangle and the lower estimate again. The same concept is that we use Ryan Point so it will be a fryer for one. Add up to half of ten

So the first question here, we're looking to calculate the lower end the upper estimates, So I'm gonna start a little lower estimates. So we know from the question that we're dividing into five different rectangles and they also be somewhat equal rectangles so there will be equal along the X axis, but not necessarily along the y axis, because we're doing five. We're gonna be going and steps of two because we're going to 10 here. So for 1st 1 we're gonna be going from this is the lower estimate. So we'll be starting on the left edge here and counting to from there and then we're gonna be doing the same thing. But for a next rectangle, we're going to start at the point where two is in our graph, and then we're gonna need going from there. And so for calculating our area from there will call that are the 1st 1 that we have there is to just cause it's two boxes and then we're gonna be adding our next one, which is six to that. And then we're gonna do the same thing. And this one is about 4.25 We'll call it doesn't have to be exact, because again, it is an estimate. So once we complete that rectangle, we're looking at about 8.5 there. And then we move on to our next one and we'll call this 15.25 again. And then that one will be at about 10.5, bringing our total up to 27. And then, from there we're gonna be doing the same thing. And we're doing our final one, which is about 6.25 again. And so will call that 1 12.5 bringing our total up to 39.5 prior. Lower estimate for the oppressed men. Time to do in different colors. You can see we are starting from the right hand side. So we're gonna go from our right hand side and that move towards the left. So that's gonna be our 1st 2 rectangle there, and that is going to be a total of six at first. And then we're gonna do the same thing with the next one, and so that one is going to start from about 4.25 So that's going to give us a total of 8.5 for that one. And then from here, we're gonna go to about 5.25 So that's gonna give us a total of 10.5. I'm sure you're noticing a trend here as well, so I won't go through. All those were just gonna calculate the next 1 12.5 And then the final one, as you can see here, is going to be just gonna count that 1234567 Someone's gonna be 14. And so when we add all that up, we're gonna have 14 points. Five that we're gonna have 25. Then we're gonna have 27.5 and then we're gonna add 14 to that given us 41.5 for upper estimate for the next question. Who were doing the exact same thing? And we're just dividing it up into groups of 10 this time. So now we're just gonna be dividing it in each low box like this, and this is gonna be our lower estimate him. We'll just do our little consolation here. And the total for that one is going to be 43.5 for lower. And for upper, it's gonna be 49.5

So we want to find the lower and upper estimates using rectangles. In the first part, we want to use five rectangles and in the second part we want to use 10 rectangles. So, as you see here in the first part, we want five rectangles, each with a width of two. Because when we take our x axis of 10 and divide it by a rectangle count of five, we get to. So as you see here, each rectangle has a with of two, and the left most corner of each rectangle is what touches the graph of F. So, as you see here, the left most point of each rectangle touches the graph for the lower estimate for the upper estimate is the opposite. In the upper estimate, we have the right most corner of each rectangle, touching the graph of F, as you see here. But we also make sure that we keep our count of five right tingles. So, in order to find the lower and upper estimates for the lower estimate, we know that each rectangle has a whiff of two so we can pull that out and multiply it by the height of each rectangle. So in the first case, we have a two pulled out. The first rectangle has a height of one plus ah, high of three plus ah, height of four point to plus ah, height of five 0.2 plus ah, high of six 0.2. And that gives us a total lower estimate of 39. The point to yeah. For us the upper estimate, we can do the same thing, but this time also pulling out the to and multiplying it by the height of each rectangle. So in the upper estimate case, we have our first rectangle of height three plus four 0.2 for the second rectangle. Close five 0.2. Excuse me for the third rectangle, plus 6.2 for the fourth rectangle and seven point and seven for the fifth rectangle. And so we have a total upper estimate of 50 1.2. So in the second case, we want to do the same thing, except we want 10 rectangles. So we divide our X axes of 10 by the number of rectangles we want, which is also 10. So 10 divided by 10 is one. So instead of each rectangle having a with of two. It'll have a with of one unit, as you see in these two cases. So for the lower estimate, like we did before, we want the left most point of each rectangle to touch the graph of F. And in the upper estimate, we want the right most corner of each rectangle to touch the graph. And so doing the calculation for the lower and upper estimate. Using Ted and Rectangles for the lower estimate. After taking the areas like we did in the first case and adding them up, we get an underestimate of 40 to 0.2, and for the upper for the other estimate For the upper estimate, we get a total of 40 eight 0.1.


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