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Respect teacher I want to make a MATLAB report on secantmethod which will approx. take 15 pages.Let me know about the data and content I have to work on and dowrite...

Question

Respect teacher I want to make a MATLAB report on secantmethod which will approx. take 15 pages.Let me know about the data and content I have to work on and dowrite an abstract, conclusion and comments for me of this report aswell.Thank you

Respect teacher I want to make a MATLAB report on secant method which will approx. take 15 pages. Let me know about the data and content I have to work on and do write an abstract, conclusion and comments for me of this report as well. Thank you



Answers

Describe the secant function.

This problem we are given a program are run and we are going thio, discuss about what this firm is doing. How is it is doing that and we're going to talk about the calculation. We are proposing these programs Mhm So we see that the user is going toe input. Three values we have the first input is a number A which is supposed to be the left and point of some interval A B. Then we have been put off him writing point off the interval AP and the number of serve intervals and in which we want to divide a B and I were supposed the of intervals has same length. So the lands off any of these of intervals when we divide and by answer intervals off the same length is B minus a over end that is the length of the interval AP divided by end. And that's the lens of any of these of intervals we obtain. Dividing a be that way. And then we're going to song values off a sequence off real numbers. And here we're going to look what are those numbers and we see that the first parenthesis here represents the sum. Then we have the sequence going from here to here. So it's thesis. Prentice's here with this one, and the sequence is represented here as the expression. First of all, is one here from here to here. And then we have a variable K which is going to take the value of the interview values from one to end. Yeah. So the sequence we're obtaining here is P minus a over end times. Why one at a plus B minus a over end. Because for cake was one we get this expression here with K equals one K was one here. The second one, which we're going to song with his previous value, is B minus a over and again times. Why one at a plus two times B minus a over. And because now we're going to put cake was, too, and so on. We're going to do that up to cables, and that is the last value is going to be B minus a over n times. Why one at a plus end, times B minus a over. And And this in this case, this expression a plus n times B minus ever end is equal to be because an is going to simplify within. So the expression is equal to a plus B minus a. Then simplify a and we get B. So this is the sum we are doing here with this sequence. Some of the sequence The sequence of value is thes value here, thes value here and the last value here and all these values are together. So these some is safe or story in viral see. And finally we displayed the the term or this oppression area equals and the value we have obtained in See, that is the song off the terms of the sequence. And now we're going to see what these terms are and why we are talking about area. Well, because So we see here this picture off the interval a b we can say that we have the first note we obtain when we divide all the whole interview with intervals off the same length and the sorry with ants of intervals of the same lens, we get B minus a over and as the lens officials of Interval, as we said here and so we have thesis. So interval the first one with this length and we know that the point here is first note after a is a plus one time that length that is a plus B minus a over. And the second one, we got to move the same distance that its be minus a over and again And we get then if we started a we got to some two times at length. That it's this point is a plus two times B minus a over. That is discretion here. Expression here is with very putting The values of K in the sequence from one to end are going to give us tea. Note that determined this of intervals. So we have for cable zero if you put zero here, we're not going to put theory in the sequence, but if we put zero here, we get a So we're not using that point we're using first is one that is a plus B minus your breath. That is for cake was one. Then we use the second one. This which is a plus two times, few minutes ever and and so on. And we saw above. The last one is going to be be that is a plus and times B minus a over. And because this expression is simplified, big previous point is a plus and minus one times be minus a over entities for cake waas and minus one. Yeah, so we are multiplying the lengthy common length B minus a over end, which is the lens off any of these of intervals times Thean image of the function at the points He's one here, this one here up to this one here and this one also. And what are the points were? Well, if we see the first into the first of interval, which is this one, we are evaluating the function ad the writing point that is a plus B minus a over end because that's the note we obtained for the first value of K, which is one that is the first known we're using is a plus B minus a over and and re evaluate their why one. And multiply that by the common land human a over end. And that multiplication represents the area for rectangle whose spaces the preventable, which has lands feminists, a rent and the height of the rectangle is the image of why one at the note at the writing point a plus B minus over. And when K goes to do the same thing for the second rectangle, that is. Its length is again being minus ever. And But the height now is why one at the writing point of that second serving tool, which is a Blust two times we minus a over and that is for K equals two. So we are multiplying the common mens of each of interval times, the image of the function. Why one at the writing points? And that's Z Ah, and that represents some off the area of Derek tangles with base disserve intervals with high tea image. Why one at the writing points? Yeah, so that's our approximation off the integral off the function between A and B or over A and B interval a B. Why one and that is approximated by the some from cake was want to end off the common length off the stove intervals we minus a over and times the function y one at the right in points of this of intervals. That is why the last writing point is in fact, be because this is the last of Interval here and it's writing point. It's B and that's just the last note we use for K equals and here. And we know the writing points are given by this expression. We A is running points, are you? But this oppression a plus k times B minus a over. And when we put in from que sorry from K, he was 12 cables en and because we are multiplying t base, the the basis off the re tangles that is through the sav intervals off in which we had divided a B times the height of their tangles. We know that is a the some of the areas of their tangles, which is going to be the approximation of the area under the graph of Y one. If I want, it's positive we could say that is an area. And then it's an approximation of the integral for maybe from a to B off the function. Why one? So that is the analysis we can do the program, which is simple one which is calculating thesis some of the areas off fruit tank, her tangles formed by taking and equal, uh, equal lengths of intervals, right, taking the basis of very tangled off. Those who've intervals are on the height of each off. Those rectangles are the images of the function y one at the writing points of the superintendents and that give us on approximation of the area off the function under the graph of the function. Why one over the interval, A. B if why wants positive? And that is because we are some of the areas off rectangles for that way.

Thank you. In this problem, we are given a program. El Ram, which produced, uh, l rhyme approximation off the function. Why one which is an approximation to the integral off dysfunction over the interval a B So the end points of the inter role a B are given here in input A m B. And we also need the number of serve intervals in which we divide a B. In our case, we're using and serve intervals off the same length. We know that the lens of those of intervals, um, is going to be the length of the holes of interval baby minus a over the numbers of intervals. And so this is the length off each of these of intervals in which we divide a B. So taking those three input the left and point of the interval a the writing point B and the number of of intervals in which we divide a B. We're going to calculate the some off the values of the sequence. And here we recognize that thes parentheses here from here is the sum off some values. The values are determined by sequence. So these parenthesis here close here, and it represents the sequence. So we give first see values or the expressions off the terms of the sequence that is Theis one and then, which is the term that is variable on this expression here, the start value on the end value. That's the way the sequence is constructed. So we can say that the general term of the sequences B minus a over n which we find here is part here. So we get thio put parenthesis, thio rapt expression, we might say, because we got to divide all the difference over end Not only a few, right, B we ever right this way. We are only dividing a by n not B minus a. So that's why, yeah, we find the parenthesis here when we were at the expression this way. But we're going to write it to explain that we're going to write it as always this way, so B minus air over, and we then identify that as a lens off each of the serve intervals, and we will apply that by the value of the function at the expression A plus K times again B minus a over end. That's what we have here. Why one at the's. Expression on. We identify the K value here, and the K value is running through the values into the values from zero to Sorry, sorry. Here from zero. Okay, from 02 in minus one. So here we have this expression here which give us the values of the sequence when we put k called 01 up two and minus one. So we have n values in total. And when we some those values. So we have to some off this expression over this range, we can say that this is a some from cable 02 in minus one, off B minus a wren, times the function. Why one at a plus K times B minus a over end. And we know that this expression is discretion. General expression for the mhm points of the sequence. We're going to analyze now what points were taking their Let's see, we have thes interval a B here in right, we have the same the first of interval off length B minus a over. And if this, uh, first note after a is a plus, that length, that is a plus B minus a over and and see that This expression here is Theis. One here with cake was one If cake will zero in this expression, here we get A which is the first point when we put cake was too. We get a plus two times the common length off the stove intervals B minus a over. And it's the same thing as saying that we some thes, same distant here, b minus a over in to get the point here, which is a plus. Two times, that is, we started a We got to some two times the length, the common length of the serve intervals. Two times we minus a over n. And if we continue this way, we're going to get for K equals and minus one. We get a blast and minus one times B minus a yoga rent. What happened? If we multiply by K equals N, we get a plus and times B minus a over. And in this expression, we're going to simplify the end and we get a plus B minus A. We simplify the A and we get be. So this expression is equal to be so. The first note correspond to K equals zero, which is a and the last note corresponds to k equals n which is speak well. So we're taking the values off the function. Why one at which note at the notes for K equals zero first, as we see here in the sequence and for K equals zero, we saw already that it's a we are evil waiting for the first interval here We're evil waiting the fortune at a so we are evaluating the function at the left and point of that's movinto. What? What happens when we put this next value of K? That is one. We are on the second interval and we are evaluating an A plus one times B minus a over. And that is thes value here, which is these and point that is again and left and point of the second serve Interval. So we are evil waiting at the left and point off each of interval in the last of interval. That is for K equals and minus one. We are evaluating at a plus and minus one B minus a over. And there is thesis point, which is this'll left Interval. So what we are doing here is calculating the some off the values obtained by multiplying the common lengths of its of Interval B minus a over 10 times the value of the function at the left endpoints of each preventable. That is why what we are attaining here. The approximation off the integral off the function over the interval over maybe the function. Why one sure. And we're using the some off the common length of the serve interval, which is a constant, so we can put it outside of thes some if you want what? We left us cease in the sequence above times thief function. Why one at the left and point left endpoints of these of intervals? Yeah, Left. Sorry. So I'm going to put it. Okay, here, left and points. So is the approximation of the, uh integral. So we can say this is a new area if if if the function Why once positive? If we assume that we know that we are approximating an area so that some that some off area of rectangles were obtaining here is going to be put in the or store in the variable C and then with play area equals and the value of see, we have obtained here. Remember, we are obtaining areas off pre tangles and some in this adding up those areas because we have a multiplication of the length of each of into which happens to be the same. Which is this one times the value of the function at the left of bone, that is the high off the rectangle is the image of why one at the left hand point of this preventable and the base of very tangle is this lens of this Vinto as each some interval has the same lens B minus saver. And that value never changes this case and only changes the value of y one at the left and points. That is why we could has said that this is the same. A speed might say You ran times to some from cable 02 and minus wine of why one at the left and points of the seven tables. Which formula is a plus K times B minus eight over end. Okay, so that the yeah, the result of this program and we could say that in general we have the input of three values. The first one is the left endpoint is of the serve Interval A. The second value input is the writing point of So the interval off the interval if integrations or a baby and the third input is the numbers of intervals, we want to divide a B in the third. In the next line were some in the values off a sequence of real numbers which are obtained by multiplying the common lens off each of the serve intervals, which is B minus a uber and times the value of the function at each of the left and points of this of intervals obtained by dividing a B into end equal serve intervals off lengths B minus ever end and that some is store or saving a verbal C, which is then display us the area under the graph of the function over the interval A. B and we know that that's the case when, why, why one is positive and is the area. It's an approximation of the area because in that case, the integral which is the values, the value we are approximating by this some here is a positive value and represents the area under the graph of Y one. So that is why we're something here the areas of rectangles, the summits approximating the total area under the graph of Y one over the interval A B And so that's the analysis we can do on this. Input this program L ra.

Okay. This question wants us to devise a method and how we'd explain how we evaluate the trig functions of any angle. So no matter the Quadrant. So the first thing we want to dio if we're evaluating the trig functions of an angle is first of all, we want to figure out what type of angle we have. So what we want to do is we want to make sure that we get Fada in our standard range, which would just be from 0 to 2 pi. And once we get data between zero and two pi, we want to figure out what type of angle and again we have our angle types that we should memorize from the first quadrant. So we have data being equal to pi over six data being equal to pi over four Seita being able to power three data being able to poverty too, or fada being able to pie. So we want to figure out which one of these denominators when we reduce our angle, it comes up with. So then once we know thes, we just evaluate the trig functions from our knowledge of the first quadrant and that gets us the magnitude. But then, for the sign, we need to check the quadrant. So we just use our pneumonic here of all students take calculus because that tells us the signs of our trig functions. So everything's positive. In quadrant one Onley, sign and cozy can are positive and quadrant to Onley. Tangent and co tangent are positive in quadrant three and Onley cosign and Sikandar positive in quadrant four. So just for a quick example, if my angle was two pi over three first we notice that that is some form of a pi over three. But this time we're in quadrant, too. Yes, And then we just evaluate this using our knowledge of the unit circle and are signs so cosine data would be negative one half because we're in quadrant too. And signed data would be positive route pre over to because we're in quadrant, too. And we could just repeat that by finding all the reciprocal functions as well. That's really the method. We just figure out what kind of angle we have with the denominator. Then we just check the quadrant to figure out where are positive and negative signs should go. Yes,


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