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Use thedefinition of a fiunction to show thst li(ax-2)-4...

Question

Use thedefinition of a fiunction to show thst li(ax-2)-4

Use the definition of a fiunction to show thst li(ax-2)-4



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Show that $\frac{\sin A}{\cos A}=\tan A$

Listen to definitions. We will prove that in general topside the rule with and serve intervals is equal to the left and point rectangular approximation method with and serve interval plus the writing point rectangular presentation method with ends of intervals And that value that's divided by two. That is perhaps of the rule is the average of the left and point and the writing point approximations. So first let's say we have uh an interval a close interval, abe interval of integration and there you have a partition formed by notes or values X zero X one up to X N. And I suppose they are orders following the index. Mhm That is a zero less than a swan less than X two and so on. Up to less than X. In venice Wanless at eggs N. In such a way that the sub intervals X zero X one X- one x 2 Eggs in -1 extend is a partition of a B. Mhm. Okay. Without we calculate all these three methods L Ramm are um and T N. So the left hand point approximation mhm. With answer vegetables is given by H times let's say first then that age okay. Mhm. Equal b minus a over and that is the common distance between any two consecutive notes. Mhm. Then we have l Ramm left and point approximation is age times a much ad 80 because in the interval X0 to expand we take the image of The left and zero as the height of derek tangle then on the interval from X one to X two we take the image of X one. That is the image of the left and point and say hi to the rectangle, can we keep on going up to the last of interval extend minus one, extend. Well we take the image of the left in point x m minus one as the height of the rectangle. So we have these and the writing point approximation. He's given us age times and now we take the image of the writing point of this of intervals as the height of their tangles. So we start with F At X one that is the highest direct angle correspond to the interval X zero X one. Then on the interval X one X two we take the image of X two that is to write a point as the height of the rectangle and we keep on going up to the last sub interval extent minus one is saying when we take the image of the writing point is in as the image of the rectangle so we have this to some so you can say that the sum of the two expressions, yeah, is equal to age, so common factor and we get all these terms plus all these terms, that is F an X zero plus f X one plus up to F At XN -1 Plus FX one know that here, I have already put these terms. Now we got to put these older terms. So if x want less. FX two plus, Let's say the term before this one here is FXN -1 plus F at X N. We have that and we can see that. Mhm. All the terms from FX one are repeated in two. In the expression that is X one effort X one is and appeared twice FX two which is a term that go next following. This appears twice. We also end. That is true. For all the terms between F of X one up to F at X n minus one. The only terms that are once our FX zero and XXN. So this will be F X zero plus two F at X one plus two. F at X two up to two. F x n minus one plus F at X 10. Here's a square bracket so it's eight times his some but this is just okay and when we take it to the same common factor or maybe if we divide by two yet, that is his son. Okay, divided by two is equal to age, half times F x zero plus two have an X one plus two, FX two plus yeah. To F X And -1 plus F X. End. And that is just now we have exactly here discretion defining to again, so this average average of the left endpoint approximation and the very impor approximation is equal to the end for any numbers of intervals and there is just what we wanted to proof Yeah.

Okay, so for probably 16 we're showing that the transpose of the transpose of the Matrix is just equal to the original matrix. And so let's start by letting, uh, each entry of a beating noted by Aye, aye. Jason's the I throw in jail column. Okay, then wth e i j Entry of the transpose is going to be equal to a J I right. And therefore, if we try to take the i j entry of the transpose of the transpose and that brings us back to a I J. But that is precisely equal to our original form of matrix. Hey. Okay, so therefore the transposed the transpose is just equal to

We have to solve that Judo point 999 up going pretty equals to one so that they started the leper insight. Do the 0.9 999 up infinity So you can date 0.9 plus Jiro pointed you on nine Cejudo point Geology wrote nine plus judo point Jiro Jiro gentle nine and plus sore I feel it right in the flex in multiply 100 10 new military and zero matter So this is nine wait 10 plus in nine way 100 plus nine by Teligent Bless nine bay Intelligent on up with infinity Take nine Going from here on Brexit will find one way Then listen nine plus one by 100 Bless one by Teligent Let's one day 10 Taligent and plus it is except up to infinity nine Break it The dumps is in genetics cities and the first meet you one day then and common issue article toe one way 10 which is less than one. So this is limit exist they would exist and we're really used as limit Find the limit with a by one minus are were a the foster an average common racial. So you this idolatry and find. So nine times in bracket A it was just one by 10 minus one minus one way Then so we'll find this. There are nine times in break it one way. 10 upon nine. Wait 10. So 10 and 10 Kinzel on a nine by nine, which is equal to one so handsome broked hand spooked.

Okay, We have this figure and we need to prove that Triangle A B G is congruent to triangle D C f. Okay, so first we'll do this graphically, which means we'll talk about it on this graph, and then you can write a to call, um, proof with the information that we come up with so we can see that b e e g Arkan grew in. So that means segment BG is can grow into segment cf. Oops. And this is addition. So Segment edition, okay. And if that's true, then we also have the third angle fear. Um, so we have angle A's congruent toe angle D angle B is congruent to angle. See all the angles in a triangle at up to 180 degrees. That means angle f is congruent angle g. So this is angle A. G B is congruent with angle D f c. And this is the third angle there. Um, okay, so now we have that the triangles are congruent from corresponding parts of congruent triangles are congruence


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