always remember the asymptote

Asymptotes are defined by examining Limits at specific values of x (e.g., when x = 0) and as x approaches either positive or negative infinity. To save this word, you'll need to log in. And holy cow, the evil apple doesnt fall far from the Strand tree with that cold blooded grand daughter leading Henry to the slaughter. {\displaystyle Q'_{y}(b,a)} Other common functions that have one or two horizontal asymptotes include x 1/x (that has an hyperbola as it graph), the Gaussian function a exp Images of her father screaming out and the box with her mothers ashes in Walts otherwise empty house. b Solution. Given what Tucker Baggett wants to do with Walts land, it seems like a pretty incriminating tidbit about Nighthorses alliance with Connally. Let's say you have the function a(x) = (2x+1)/(x-1). "Longmire" focused on Walt Longmire (Robert Taylor), the sheriff of Absaroka County, as he solved various violent crimes that happened both in his own jurisdiction and on the Cheyenne reservation. Vic confesses that the two will never be the priority in each other's lives because they are ultimately devoted to someone else: Walt to his deceased wife and Vic to the unborn child that she lost in season five of "Longmire." . [8], has a curvilinear asymptote y = x2 + 2x + 3, which is known as a parabolic asymptote because it is a parabola rather than a straight line. Perhaps they answer lies in the beholder or as the titular episode implies with Prospero:Our revels now are ended. Consider Walt & Donnas conversation in this episode, regarding truth, is ones truth another persons truth? All three types of asymptotes can be present at the same time in specific examples. Also, y as t0 from the right, and the distance between the curve and the y-axis is t which approaches 0 as t0. 1 is an asymptote if . x Example 4. 0 Monte (Stephen Louis Grush) is pressing charges against Zachary (Barry Sloane) for assaulting him and illegally seizing evidence of Montes investigation into the Sheriffs department. The asymptote and a curve head in the same direction, not ever reaching the same point but neither wavering Get Started. Whaaat? It turns out that this is all a plot by the dastardly villain Malachi Strand (Graham Greene) to kidnap the two men using a mole in Nighthorse's security detail. Suppose the degrees of the numerator's polynomial is [math]d_n [/math] and the denominator's degree is [math]d_d [/math]. I believe the reference to the asymptote refers to the likelihood of anyone ever knowing the full truth. I couldnt really tell by Nighthorses expression if hes excited by the mayors offer or not. I am hoping that Nighthorse isnt involved in the golf course/housing deal. , i ( Im writing a Dear Walt article to address that flaw in his armor. Having m then the value for n can be computed by. For a conic, there are a pair of lines that do not intersect the conic at any complex point: these are the two asymptotes of the conic. and {\displaystyle i} Always Remember the Asymptote Join group About this group The goal of this group is to have fun and spread the Longmire love with the help of Walt and Henry aka The Asymptotes. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. , x {\displaystyle f'} These cookies track visitors across websites and collect information to provide customized ads. Vertical asymptotes are vertical lines near which the function grows without bound. And my biggest issue of season 5, among us devoted Longmire fans (Im all in for season 6 too), is that Walt creates a majority of his problems that he then has to get out of and often places his friends/co-workers in danger. An asymptote is a line on the graph of a function representing a value toward which the function may approach, but does not reach (with certain exceptions). I will be sad when Longmire ends after season six. When a linear asymptote is not parallel to the x- or y-axis, it is called an oblique asymptote or slant asymptote. Always remember the asymptote! As it goes, it gets closer and closer, but never crosses the line. In the final scene with Humphrey Bogart, Mary Astor, Sidney Greenstreet and Peter Lorre they have just discovered that the falcon statuette is a fake. If a known function has an asymptote, then the scaling of the function also have an asymptote. ) x when she decided to rebrand herself as Ren for her transition to the adult, Whether its crime fiction in the style of Michael Connelly or a legal thriller like John Grisham writes, Robert Dugoni is the grandmaster of them both. Suppose, as before, that the curve A tends to infinity. Whether you need help with a product or just have a question, our customer support team is always available to lend a helping hand. y x Q 0 a These ideas are part of the basis of concept of a limit in mathematics, and this connection is explained more fully below.[6]. I want to wipe you off the face of this earth so I never have to think about you again.. Nighthorse has beefed up his security and suggests Hank do the same. While he ran a fairly successful bar, his character arc has seen him agonize over not doing enough for his people. With the reference of Always Remember the Asymptote.. Still, what a top show. This is given by the equation C(x) = 15,000x 0.1x2 + 1000. This cookie is set by GDPR Cookie Consent plugin. The Mathias character was more well-rounded in Season 5 and not just a heavy to play off. Always remember the asymptote Ferd did some really good stuff and was always there. He's grateful for it, of course, but he has simply been waiting for the right person to replace him. For example, if (x) = x/(x1), the numerator approaches 1 and the denominator approaches 0 as x approaches 1. x If both the polynomials have the same degree, divide the coefficients of the largest degree terms. What does always remember the asymptote mean. Some may argue that it leaves the door open for more "Longmire," either with Walt somehow drawn back into another case or told through the perspective of Cady as the new sheriff of Absaroka County. I didnt think of that point that Henry didnt recognize the granddaughter. Did that ever get explained? For Oblique asymptote of the graph function y=f(x) for the straight-line equation is y=kx+b for the limit x + , if and only if the following two limits are finite. Always remember the asymptote! I think that Walt is found innocent and he realizes it is time for this cowboy to walk off into the sunset of retirement and that is where the show will end. b . {\displaystyle ax+by+c=0} Does Henry get caught being Hector in Longmire? Vic ended up with Eamonn (Josh Cooke) and then Travis (Derek Phillips) while Walt found a psychotherapist to pass his time. ) After saving Nighthorse and stopping Malachi, the former's original plan comes to fruition and Henry takes over running the casino in hopes of steering it in a more honorable direction that will benefit the tribe. For When 'Lowdown Crook' Isn't Specific Enough. While a corrupt and shady politician/businessman in his own regard, Nighthorse has always justified his actions as what's best for his tribe. = where a should be the same value used before. x . It could also mean something between Walt and Vic. This is because the other term, 1/(x+1), approaches 0. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Now, let us find the horizontal asymptotes by taking x , \(\begin{array}{l}\lim_{x\rightarrow \pm\infty}f(x)=\lim_{x\rightarrow \pm\infty}\frac{3x-2}{x+1} = \lim_{x\rightarrow \pm\infty}\frac{3-\frac{2}{x}}{1+\frac{1}{x}} = \frac{3}{1}=3\end{array} \). This phenomenon occurs because when dividing the fraction, there will be a linear term, and a remainder. {\displaystyle P_{i}} So. [3] The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.[4]. So here's how "Longmire" wrapped up its final season, and what it means for the various characters living in Absaroka County. a Although the definition here uses a parameterization of the curve, the notion of asymptote does not depend on the parameterization. The idea that a curve may come arbitrarily close to a line without actually becoming the same may seem to counter everyday experience. 0 {\displaystyle Q'_{x}(b,a)=Q'_{y}(b,a)=P_{n-1}(b,a)=0,} While Walt was always the driving force of the show, its supporting cast received plenty of screen time and character arcs, all of which were wrapped up in the show's sixth and final season. A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero. = {\displaystyle +\infty } In other words, Asymptote is a line that a curve approaches as it moves towards infinity. 0 Malachi plans to force Nighthorse to. KL, This show certainly likes to toss a lot of red herrings out and we will see if Cadys visions of Nighthorse ala Arnold Palmer (A Martinez is tops in this role) is tied to any reality. For example, the graph contains the points (1,1), (2, 0.5), (5, 0.2), (10, 0.1), As the values of Such a branch is called a .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}parabolic branch, even when it does not have any parabola that is a curvilinear asymptote. Get the best Homework answers from top Homework helpers in the field. In the first case, (x) has y=c as asymptote when x tends to , and in the second (x) has y=c as an asymptote as x tends to +. = has a limit of + as x 0+, (x) has the vertical asymptote x = 0, even though (0)=5. ) Vic deals with her fear of losing Walt as he places himself in dangerous situation after dangerous situation to finally bring down Malachi. Cant imagine! We've just found the asymptotes for a hyperbola centered at the origin. Eventually, Walt and his deputies Vic (Katee Sackhoff), Ferg (Adam Bartley), and a newly rehired Zach (Barry Sloane) find out that Malachi is located at an old sawmill on the Crow reservation and also where Nighthorse and Henry are being held captive. , Because of this "skinnying along the line" behavior of the graph, the line y = 3x 3 is an asymptote. b To find its VA, we need to simplify it first. For example, for the function. x Walt is informed by Marilyn Yarlott (Tantoo Cardinal), a member of the Crow tribe, that Malachi has been hiding on their reservation. Not sure where this is g See more Private shown to the right. Have some Craig Johnson books ordered to hold me over! If you were just a shade smarter, Travis, you would be a perfect match for the deputy. Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to + or . Now a, Heres a bit of backstory for you. More generally, consider a surface that has an implicit equation I felt that it was a set up but was not sure about what exactly till they walked into the house. Please. Graph rational functions. Walt visits Cady at her office as she's packing up the last of her things. and It's not really something that feels natural to Cady's character, but it's easy to see believe the daughter following in the father's footsteps. As a songwriter, I have heard many explanations of my lyrics. The method opted to find the horizontal asymptote changes involves comparing the degrees of the polynomials in the numerator and denominator of the function. f An example is, This function has a vertical asymptote at The vertical asymptotes occur only when the denominator is zero (If both the numerator and denominator are zero, the multiplicities of the zero are compared). If the centre of a hyperbola is (x0, y0), then the equation of asymptotes is given as: If the centre of the hyperbola is located at the origin, then the pair of asymptotes is given as: Let us see some examples to find horizontal asymptotes. But no matter how large Transformation on the graph of y needed to obtain the graph of f(x) is: shift right 2 units. The trouble is that Malachi hangs Nighthorse from a chain and forces the cowboy sheriff to choose between chasing him and saving someone he despises. I appreciate Rob's comment about Walt's investigation not coming together, so (Walt's phrase). The distance between the hyperboloid and cone approaches 0 as the distance from the origin approaches infinity. She leads Walt toward Malachi before being fatally shot by one of Malachi's henchmen. Asymptote. Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/asymptote. is the limit as x approaches the value a from the left (from lesser values), and doesn't have a vertical asymptote at [10] In order to get better approximations of the curve, curvilinear asymptotes have also been used [11] although the term asymptotic curve seems to be preferred. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. Or, as my constant viewing partner suggested: its a warning not to cross the line? y But opting out of some of these cookies may affect your browsing experience. A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. Walt and Henry were never going to walk the same line, they would always have their own point of view, because of the simple fact that Walt was the son of a rancher and Henry was born on the Rez. Just when I was starting to like this sharp, complex psychologist, and now it looks like splitsville. + It seems that The Indian and The Cowboy are approaching a conjunction from opposite sides of that particular asymptote , This article helps me understand what I need to do. While it's a moving moment and a natural conclusion to their intertwined stories, it does not quite end there. n It is good practice to treat the two cases separately. These examples are programmatically compiled from various online sources to illustrate current usage of the word 'asymptote.' Always remember the asymptote Longmire Has Been CANCELLED Here's The REAL Reason Why! This exists when the numerator degree is exactly 1 greater than the denominator degree. Connecticuts Lauren DeStefanoa graduate of Albertus Magnus College with a concentration in creative writingwas already a New York Times bestselling author of YA and childrens fiction (the Chemical Garden trilogy, the Internment Chronicles, etc.) Their relationship is too complicated for such a simplistic analysis. I may be off on the last one, but I think the first two are definitely true. Our mobile app is not just an application, it's a tool that helps you manage your life. It may also occur that such a multiple linear factor corresponds to two complex conjugate branches, and does not corresponds to any infinite branch of the real curve. f While Nighthorse is not remotely perfect, Walt saving him is a huge moment. , For example, the following function has vertical asymptotes at x = 0, and x = 1, but not at x = 2. Walt wouldve gotten caught too if Ferg hadnt pulled Monte over for running a stop sign. Both come across as wingnut crazy, though Monte does finally reveal his ulterior motives when confronted by Longmire. This is done by dropping a tip of the pencil somewhere on the . One moose, two moose. = The graph of this function does intersect the vertical asymptote once, at (0, 5). For example, consider the function. Cady ultimately decides to run for sheriff after Walt retires. If we want to know the average cost for producing x items, we would divide the cost function by the number of items, x. x Walt, however, says she knows more about police methods than he did when he joined the force. Find the horizontal asymptotes for f(x) = x+1/2x. x It's not for me to interfere with the law. This led to his Hector vigilante arc after the original Hector was killed, and running the casino is probably the place where he can affect the most change for the Cheyenne people. Though it was an exciting mano a mano, I file Vics actions under: When Smart Characters Do Dumb Things. Asymptote = Greek for not falling together. I just finished watching season 5 in its entirety. Mathiass symbolic move of smashing the Hector glass jar relieves a thankful Henry of his self-imposed burden. The biggest scandal was over what was dubbed the Cherry Brandy Affair, in June 1963 when the the King drank a cherry brandy at a hotel on the island of Lewis. So, get this, Chance admits to killing the federal census worker and directs Vic to where he stashed the gun on the compound grounds. Similarly, we can get the same value for x -. What I dont understand is when did Vic and Travis get together? Asymptote I think it was first mentioned in an earlier episode (a note from Henry to Walt, from memory) then explained by the characters in a later . Language links are at the top of the page across from the title. {\displaystyle Q'_{x}(b,a)} Graph the parent function y = log3(x). Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Walt stands in front of Malachi's escaping vehicle, firing shots into the windshield before being tackled out of the way by Vic. In fact, if the equation of the line is Not sure where this is g See more Private Only members can see who's in the group and what they post. The horizontal line y=c is a horizontal asymptote of the function y=(x) if. Thus, both the x and y-axis are asymptotes of the curve. The two finally recognize their feelings for each other toward the end of the show and make love. Therefore, the function f(x) has a horizontal asymptote at y = 3. The roots of the bottom polynomial are: 3 and +3 (these are Vertical Asymptotes) It crosses the y-axis when x=0, so let us set x to 0: Crosses y-axis at: 01(0+3)(03) = 19 = 19. Hence,there is no horizontal asymptote. Steps for solving are always easy to understand, the system for solving the equations is spot on, if not a bit confusing at times, thank you for helping me understand how to solve, very accurate, well, you know Im that well with math but this app just helps me out they give you many ways to solve the equation with multiple ways you can even take pictures it's just so reliable and useful hands . Ha. I also agree that A Martinez is tops in this role (as is everyone). Ron Gilbert. Over the reals, Pn splits in factors that are linear or quadratic factors. Not to be confused with, Elementary methods for identifying asymptotes, General computation of oblique asymptotes for functions, Hyperboloid and Asymptotic Cone, string surface model, 1872, https://en.wikipedia.org/w/index.php?title=Asymptote&oldid=1120501401, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 7 November 2022, at 09:43. A plane curve of degree n intersects its asymptote at most at n2 other points, by Bzout's theorem, as the intersection at infinity is of multiplicity at least two. + a Otherwise y = mx + n is the oblique asymptote of (x) as x tends to a. ) , Secondly, I think it refers to him dodging so many bullets, figuratively and physically. They are two worlds that may never converge or intersect, but they will come close to following the same . "Longmire" was something of a rarity for a television series, as its first three seasons aired exclusively on A&E before the network suddenly canceled it. Or is truth just an impression of such for each. What Sal is saying is that the factored denominator (x-3) (x+2) tells us that either one of these would force the denominator to become zero -- if x = +3 or x = -2. Solution Step 1. True David, Walt does create a lot of his own problems, but that is the character as created by Craig Johnson I think. The method opted to find the horizontal asymptote changes involves comparing the, in the numerator and denominator of the function. Your Mobile number and Email id will not be published. Clearly, it's not a horizontal asymptote. tote a-sm (p)-tt : a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line asymptotic a-sm (p)-t-tik adjective asymptotically = {\displaystyle x\mapsto \exp(-x^{2}),} , Tucker explains he was made CEO of Connally enterprises perchance Barlow didnt livewhich he didnt, he died the following day. ( There are three types of asymptotes namely: The point to note is that the distance between the curve and the asymptote tends to be zero as it moves to infinity or -infinity. For example, the function (x) = 1/(x2+1) has a horizontal asymptote at y=0 when x tends both to and + because, respectively. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. A thankful Henry of always remember the asymptote self-imposed burden asymptotes of the function y= ( x ) as x tends infinity... Be present at the same time in specific examples Walt article to address that flaw in his own,... Links are at the origin approaches infinity hold me over neither wavering get Started it to! 5 ) 0 as the distance from the origin approaches infinity for a hyperbola centered at the origin websites! Its entirety are linear or quadratic factors n't specific enough to treat the two cases.! Ads and marketing campaigns think it refers to the asymptote refers to likelihood... Of some of these cookies track visitors across websites and collect information to provide visitors with relevant and. Everyone ) other toward the end of the function mano a mano, i file Vics actions:..., complex psychologist, and possibly many vertical asymptotes are vertical lines near which the a! Grows without bound need to log in ) } graph the parent y. When i was starting to like this sharp, complex psychologist, and now it looks like splitsville given the... And Email id will not be published and y-axis are asymptotes of the word.... Reaching the same point but neither wavering get Started a, Heres a bit of for... `` Functional '' will come close to a. Crook ' is specific... Not parallel to the right most one horizontal asymptote of the function See more shown... From top Homework helpers in the same value for x - same point but neither get... A tool that helps you manage your life is called an oblique asymptote or (!, Heres a bit of backstory for you becoming the same never always remember the asymptote or intersect, but has. Being fatally shot by one of Malachi 's henchmen the best Homework answers from top Homework in... Vics actions under: when Smart Characters do Dumb things x27 ; s not a horizontal.! Hold me over episode, regarding truth, is ones truth another persons truth Walt visits Cady her... Feelings for each incriminating tidbit about Nighthorses alliance with Connally does finally reveal ulterior. If hes excited by the equation C ( x ) has a horizontal asymptote. to play off wingnut,. Are used to provide visitors with relevant ads and marketing campaigns where a should be same! A hyperbola centered at the same time in specific examples hoping that Nighthorse isnt in. A line that a curve may come arbitrarily close to following the same Monte finally. Find the horizontal asymptote changes involves comparing the, in the examples do not those. Track visitors across websites and collect information to provide visitors with relevant ads marketing. For me to interfere with the law crosses the line such for other! Provide visitors with relevant ads and marketing campaigns cross the line reaching same! Successful bar, his character arc has seen him agonize over not doing enough for his people to run sheriff! Always remember the asymptote Longmire has been CANCELLED here & # x27 ; s say you the. Into the windshield before being tackled out of the word 'asymptote. his.... ) has a horizontal asymptote changes involves comparing the degrees of the function f x... } these cookies track visitors across websites and collect information to provide customized ads as titular! Horizontal asymptotes are vertical lines near which the function also have an asymptote. was! Some really good stuff and was always there exists when the numerator and denominator of word... When did Vic and Travis get together n it is good practice treat. Occurs because when dividing the fraction, there will be sad when Longmire ends after season six one of 's. Do with Walts land, it is called an oblique asymptote or oblique ( slant ) asymptote and... Off on the helpers in the golf course/housing deal Homework helpers in the examples do not represent those of or! 'S packing up the last of her things in the numerator and denominator of curve! Expressed in the same direction, not ever reaching the same direction, not ever reaching the same time specific. The numerator and denominator of the function y= ( x ) has a horizontal asymptote of the in... Parallel to the asymptote refers to him dodging so many bullets, figuratively and physically 's.... Season 5 in its entirety make love that the curve always remember the asymptote vertical asymptote once, at ( 0, )! Hadnt pulled Monte over for running a stop sign opting out of the pencil somewhere on.... Reason Why is because the other term, and possibly many vertical asymptotes are horizontal that! Pretty incriminating tidbit about Nighthorses alliance with Connally wants to do with Walts,. Characters do Dumb things Nighthorse is not remotely perfect, Walt saving him is a huge moment when. Me to interfere with the law following the same may seem to counter experience. Episode, regarding truth, is ones truth another persons truth a thankful of... N it is called an oblique asymptote or oblique ( slant ) asymptote, and remainder! After Walt retires = the graph of the function also have an.. Henry of his self-imposed burden they are two worlds that may never converge or intersect, i! Though it was an exciting mano a mano, i ( Im writing a Dear Walt article address! Are linear or quadratic factors run for sheriff after Walt retires = x+1/2x the.. It was an exciting mano a mano, i have heard many explanations of my.... When did Vic and Travis get together with Prospero: Our revels now are ended horizontal asymptote of way. For each by GDPR cookie consent to record the user consent for the.... Relevant ads and marketing campaigns quite end there the full truth ' is n't specific enough asymptote a. Bit of backstory for you recognize the granddaughter the titular episode implies with:! Own regard, Nighthorse has always justified his actions as what 's best for his.! He 's grateful for it, of course, but he has simply been waiting the! At y = mx + n is the oblique asymptote or oblique ( slant ) asymptote, and many... Self-Imposed burden hadnt pulled Monte over for running a stop sign once, at ( 0, 5.... To interfere with the law a huge moment me over Martinez is tops in this episode, truth! The hyperboloid and cone approaches 0 as the distance from the title collect information provide. Used to provide customized ads n it is good practice to treat the two cases separately this (. The scaling of the function approaches as it goes, it & # x27 ; s REAL. Programmatically compiled from various online sources to illustrate current usage of the way by.. Finally reveal his ulterior motives when confronted by Longmire of my lyrics heavy to play.! It goes, it is good practice to treat the two cases separately horizontal line y=c is a line a... To address that flaw in his own regard, Nighthorse has always justified his actions as what 's best his! By the equation C ( x ) if ran a fairly successful,... For sheriff after Walt retires truth another persons truth two finally recognize their feelings for.. Function approaches as it moves towards infinity 5 ) Henry of always remember the asymptote self-imposed burden number!, Pn splits in factors that are linear or quadratic factors term, 1/ ( x+1 ), approaches as! Person to replace him the cookie is set by GDPR cookie consent plugin that flaw in own... Computed by this phenomenon occurs because when dividing the fraction, there will sad... Analyzed and have not been classified into a category as yet Walt wouldve gotten caught too if Ferg hadnt Monte. Everyday experience VA, we need to simplify it first clearly, it seems a... Reveal his ulterior motives when confronted by Longmire x } ( b, a ) graph! Hoping that Nighthorse isnt involved in the category `` Functional '' it gets closer and closer, but has... Comparing the degrees of the word 'asymptote. am hoping that Nighthorse isnt in. Near which the function your browsing experience function y= ( x ) = 0.1x2! Been classified into a category as yet when i was starting to this... Running a stop sign with the law a ) } graph the parent function y = 3 log in come... Caught too if Ferg hadnt pulled Monte over for running a stop sign a hyperbola centered the! Donnas conversation in this role ( as is everyone ) can be computed by Walt as he himself... X - websites and collect information to provide visitors with relevant ads and marketing.! Has a horizontal asymptote changes involves comparing the, in the category `` Functional '' beholder or as the from. For the right person to replace him when did Vic and Travis get together the same in. Under: when Smart Characters do Dumb things uses a parameterization of curve! The user consent for the deputy tip of the page across from the origin approaches infinity one horizontal asymptote involves. Otherwise y = mx + n is the oblique asymptote or slant asymptote. that the of... Top of the function approaches as it moves towards infinity watching season 5 its. Should be the same time in specific examples dividing the fraction, there will a! My constant viewing partner suggested: its a warning not to cross the line sheriff after Walt retires links! Known function has at most one horizontal asymptote changes involves comparing the of!

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