This is disorganized. But I thought it had potential. Can you take the slope of a point and the start of the graph and the slope at the end of the graph and combine it with an approach similar to Newton's Method, to determine where a given value occurs?

I know it sounds stupid, but I am serious. I haven't had a calculus course in 20 years. But if you look at the picture (which is also messy), it just might give you some ideas.

The problem starts out to find a limit. On a graph the limit of the relative minimum is the desired value. Limit notation finds a limit 0 (zero) when x equals a known value. But it would be more useful to find the value of x when the limit equals zero. So instead of finding the limit at a given value, the goal is to find the value at a given limit.

Is there a method for this? The only methods I know is to test the values until the desired point is revealed. Newton's Method may prove helpful. However test values are still need.

The question is how do you find x when the y value is known, where y is the limit (zero in this case).

This idea is in early stages. It is just a concept. But my question is as you look at the picture can you create useful geometry that combined with the integral and derivative can be used to map a graph?

I know this is messy, but when you read it, it just might give you some good ideas.

2 hours ago, Trurl said:

This is disorganized. But I thought it had potential. Can you take the slope of a point and the start of the graph and the slope at the end of the graph and combine it with an approach similar to Newton's Method, to determine where a given value occurs?

I know it sounds stupid, but I am serious. I haven't had a calculus course in 20 years. But if you look at the picture (which is also messy), it just might give you some ideas.

I am going to say +1 for this, crediting you with having come up with the idea by yourself.

There is a considerab;le wealth of important mathematics that has been developed about this, although as you might guess it does not work out quite as you say.

Calculus is often involved and it touches many aspects of applied maths.

Curve fitting
Extremal points
Finite element analysis.
Boundary element analysis

To name but a few

Can you please tell us what is your actual interest so that that we can help pointing you in the right direction ?

Edited June 22Jun 22 by studiot

@studiot Thanks for the reply. The problem I am facing is that I can find the value of the limit knowing x, but I want to find x as the limit approaches zero.

I know the equation of the function should be able to be set to zero, but on a curve I can’t get it to work. I was trying to create enough information with the derivative to “make it work.”

I have seen others “program” this with trial and error, but is there a known method? This is a reoccurring problem for me. Others can inspect the graphs better than I can and I made the graph. It does apply to Simple Yet Interesting. But I have moved past that problem. But the challenge of knowing x at a given limit still exists. I don’t know what the solution is. But I truly believe the answer unleashes some dynamic way to approach graphs.

We have all heard of the Batman Equation.

Click Here https://m.youtube.com/watch?v=oaIsCJw0QG8&pp=ygUaYmF0bWFuIGVxdWF0aW9uIHJldmlzaXRlZCA=

The Batman equations add parametric equations together. As the video states any design of more complexity takes a computer.

But what if we could solve the equation both parametrically and using Cartesian Coordinates? I know that with some equations you are left with things that aren’t very useful. But if the complex was made simple you could determine where a certain value takes place.

I mentioned that I wanted to start a make-shift bio lab. I am not a biologist, but I wanted to read more to understand the pattern of DNA. I figured if an irregular, complex pattern could be described by a helix then what else can be described by matching an equation to a pattern? I figured a logarithmic spiral could be used to describe Prime numbers. My figuring is that if you force a pattern to a shape then that shape may reveal patterns of the series.

That is where drawing “irregular” shapes and being able to covert and map the shape’s coordinates comes in.

What if we were to graph an equation y = 7x + 5 ?

But what if a graph y = 7x + 5g, where g is a set of numbers {3, 5, 7, 11, 13…}

g doesn’t have to be a variable; it can be a derivative, integral, or equation; it doesn’t even have to be linear.

If I control what g is, can I force at pattern? Can I give order to a drawing or sketch without a super computer?

And of course you could at more variables other than g or even program variables with variables.

I know it sounds too abstract or too complex. I hope I explained it right. One of the images in a graph was Newton. The Newton sketch takes much processing power to draw. But I just thought nesting equations with equations could simplify the entire process.

Again I know this idea is abstract. It isn’t a solution. Instead it is a thought process. I don’t know the methods of these maths. I am just sharing how I would go about trying to solve such problems.

*note the Newton drawing is in the linked YouTube video.