Asymptotes of a curve

Question

Hello my friends

I have two main concerns
1) How to draw an asymptote (vertical, horizontal, and oblique) to a curve in Excel. Example: f(x)=(x^2-4)/(2x+1)?
2) How to chat online on our favorite site howcamarche.net? How to directly ask a question to a friend online and get the answer almost instantly?

yg_be · Answer

Hello,
how did you plot the curve of the function f(x) in Excel?
are you wondering how to calculate the asymptote, or how to plot it?

the site commentcamarche does not offer an option for instant discussion between two people.
the best way to get a quick response is to know and follow the guidelines, be precise and factual, and provide all the useful information.

Raymond PENTIER · Answer

Hello acacia; hello yg_be.  There is an important piece of information missing: as x approaches what value? The method will consist of adding a column to your table in which you will calculate the values of y. Assuming you let x approach infinity, you first need to calculate the limit of your fraction, which is x²/2x thus x/2; your additional column will therefore contain the values of a=x/2.  You are registered as a member, so you can send a Private Message to another member. If you want a nearly instant response, you should send this message to them while they are on their computer.  -- It’s nice, retirement! Especially in the Caribbean... Raymond (INSA, AFPA)

Pierr10 · Answer

Hello everyone

I don’t quite understand what you want to do.

- If it’s about finding the equations of the asymptotes using Excel, I don’t think that’s possible. But since I’m not an Excel specialist, I don’t want to make any assumptions.

- If it’s about plotting the asymptotes, you first need to determine their equations by calculating them by hand and then fill in the table.
I think determining the equations isn’t your problem.
To me, all this is a little bit distant, but if I’m not mistaken, there are:
A “vertical” asymptote with the equation x = -1/2
An oblique asymptote with the equation y = x/2 - 1/4

I made a quick graph with the curve and only the oblique asymptote.
(For the “vertical” asymptote, I’m not sure if that’s possible).
The type of graph to use is “scatter plot” and there are 2 series of points. It looks like this:

I didn’t connect the points, otherwise Excel wouldn’t hesitate to connect the two parts of the curve (just like calculators do, by the way).

As for private messages, yg_be and Raymond Pentier, whom I greet, have already responded. Help in private messaging isn’t in the spirit of the forum because the help we provide to some can serve other members, sometimes much later.

Raymond PENTIER · Answer

Hello, acacia.  It has been about fifty years since I last dealt with limits and asymptotes. Therefore, you should trust Pierr10's answer more, which seems perfectly reliable to me. I take this opportunity to greet him warmly.   -- Retirement is nice! Especially in the Caribbean... Raymond (INSA, AFPA)

Raymond PENTIER · Answer

Small addition for acacia.  There is a vertical asymptote when y approaches infinity, which occurs when the denominator of the fraction approaches zero, so here when x approaches -1/2. The vertical asymptote is the line with the x-coordinate -0.5.  There is a horizontal asymptote if y approaches a constant when x approaches plus or minus infinity, which is not the case here, where the fraction approaches x/2, which is not a constant. -- Retirement is great! Especially in the Caribbean... Raymond (INSA, AFPA)

Pierr10 · Answer

Hello,

I will respond for function 1). You should be able to transpose for function 2).

First of all, I want to say that to my knowledge, there is no simple solution to trace vertical asymptotes. Everything I manage to do looks like a makeshift solution. Perhaps Excel experts have solutions.
You want to create a chart that includes 4 parts: the 2 branches of the curve and the 2 asymptotes. So there will need to be 4 data series.
I proceeded as follows:
One data series for x going from - infinity to x=-1 (exclusive)
One data series for x going from x=-1 (exclusive) to + infinity
One data series with y = 1 for the horizontal asymptote
One data series with x = -1 for the vertical asymptote. It's this one that poses a problem.

Since it's not really complicated but tedious to explain, I'm providing a link so you can access the Excel file.

https://www.cjoint.com/c/IHDoxZJvsEK

In column B, the x values incrementing by 0.1 unit.
In C and D, the 2 parts of the curve. The split is done with an IF function.
In E, the value 1 for the horizontal asymptote
In E, the value -1 for the vertical asymptote.

We select the first 4 columns and insert a scatter plot. (The graph needs to be completely edited, so what we select initially is of little importance).
The resulting graph looks like nothing.

We right-click on the graph and choose Select Data.
The first branch of the curve corresponds to series 1. We choose Edit and select the useful range of values (be sure to exclude the row corresponding to x = -1)
We do the same for series 2 and for series 3 (horizontal asymptote).
We add a series for the vertical asymptote and choose the values from column F for x values. Column B contains the y values. It's makeshift. Might as well add a line by hand.
When all the data is correct, we click OK and the graph should appear.

For the second function, you will do the same. Be careful, the equation of the oblique asymptote is incorrect: it is y = 2x + 2

Best regards

ccm81 · Answer

Hello everyone  A (small) example for tracing the first function. You can change the values of xmin, xmax, step https://mon-partage.fr/f/b1l2Pudp/  Best regards

Raymond PENTIER · Answer

Good evening acacia1952.  Now that ccm81 and Pierr10 have solved your problem for the first function, here is the one for the second: in red, with your oblique asymptote formula; in purple, with Pierr10's formula. -- Retirement is great! Especially in the West Indies... Raymond (INSA, AFPA)

ccm81 · Answer

And while we're at it, a solution for problem 2 https://mon-partage.fr/f/BWwy4SiC/  We can modify the yellow cells  Best regards

Asymptotes of a curve

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