/sci/ - Science & Math » Thread #12861223

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Anonymous Sun 21 Mar 01:44:32 2021 No.12861223 View Reply Original Report

Quoted By: >>12861238 >>12861241 >>12861277 >>12861924

When delta x goes to zero, does the plot on the Cartesian plane go from a dot to a vertical line?

Will this help me understand natural logarithms? Before going from 3, not 2.99999999 or 3.00000001, but going from 3 to 4, the vertical line needs to rotate a little and become a small dot? So you have a little more effort needed for continuity than just sequentially counting integers.

Anonymous

Anonymous Sun 21 Mar 2021 01:51:00 No.12861238 Report

Quoted By: >>12861256

>>12861223
wat

Anonymous

Anonymous Sun 21 Mar 2021 01:52:04 No.12861241 Report

Quoted By:

>>12861223
b'scuse me?

Anonymous

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Anonymous Sun 21 Mar 2021 01:57:13 No.12861256 Report

Quoted By: >>12861268 >>12861305 >>12861324

>>12861238
So this is the Cartesian plane. Normally you plot dots at values of (x,y). But in Calculus, you want delta x to go to zero. So if that's the case, do you have vertical lines instead of dots?

And is that why you have this "hidden" function of the integral of 1/x? If you were just using a normal summing function of (x*1/x), like (2*1/2), (3*1/3), you just get a straight line. But with logarithims, you have to take into account continuity, going from straight vertical line at x, to dot at x.

Anonymous

Anonymous Sun 21 Mar 2021 02:01:13 No.12861268 Report

Quoted By:

>>12861256
And does that help explain the relationship between e and pi?

pi is based on the circle. e is based on going as small as you can go, taking as many right angle turns as you can go.

Anonymous

Anonymous Sun 21 Mar 2021 02:05:00 No.12861277 Report

Quoted By: >>12861298

>>12861223
>absolute value on x
pleb

Anonymous

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Anonymous Sun 21 Mar 2021 02:15:36 No.12861298 Report

Quoted By:

>>12861277
It's clarifying to me that they're different and it takes something to go from one to another.

Anonymous

Anonymous Sun 21 Mar 2021 02:19:28 No.12861305 Report

Quoted By: >>12861343

>>12861256
>So this is the Cartesian plane. Normally you plot dots at values of (x,y). But in Calculus, you want delta x to go to zero. So if that's the case, do you have vertical lines instead of dots?
Umm, sort of. You can't really plot "infinitely small" things, so you plot them as lines of finite length. But there's really nothing to it, you won't get any deep insight thinking about that stuff.

>If you were just using a normal summing function of (x*1/x), like (2*1/2), (3*1/3), you just get a straight line.
x is not dx, so your argument doesn't make a whole lot of sense.

>But with logarithims, you have to take into account continuity, going from straight vertical line at x, to dot at x.
No idea what you mean

>pi is based on the circle. e is based on going as small as you can go, taking as many right angle turns as you can go.
no

Anonymous

Anonymous Sun 21 Mar 2021 02:29:35 No.12861324 Report

Quoted By: >>12861353

>>12861256
>But in Calculus, you want delta x to go to zero. So if that's the case, do you have vertical lines instead of dots?
No, you have tangent lines to the curve you're measuring. It's true that
$\lim_{?x \to 0} f(x) = \frac{f(x+?x)+f(x)}{?x}$
but as ?x approaches zero, while it's true that the denominator's becoming very small makes the numerator much bigger, the difference between f(x+?x) and f(x) will also become very small, meaning the derivative is not necessarily undefined (i.e. a vertical line).

Anonymous

Anonymous Sun 21 Mar 2021 02:34:56 No.12861343 Report

Quoted By: >>12861951

>>12861305
> But there's really nothing to it, you won't get any deep insight thinking about that stuff.

I was thinking of Planck's constant in physics. That little bit of energy is going from a vertical line segment to a dot. I was also thinking of Navier Stokes problem of continuity, if you could solve it by using something like a phonon, and saying if it has viscosity, it has phonons, and from there a model that's only electromagnetic without masses, no conduction or convection.

> x is not dx, so your argument doesn't make a whole lot of sense.

yes, you're right, thank you. I was thinking the derivative of x^1 is a constant, and you need logarithms to get the integral of 1/x

so it's the sum of output*(input2-input1), not the sum of output*input. That still means something different if you assume continuity.

> e is based on going as small as you can go, taking as many right angle turns as you can go.

(1+ 1/?) ^ ?

That 1/? is as small as you can go. That ^ ? is as many right angles as you can go.

Anonymous

Anonymous Sun 21 Mar 2021 02:37:53 No.12861353 Report

Quoted By:

>>12861324
ok, so there's still values in the derivative. got it.

Stuff could still happen without affecting the derivative though, right? If a spring is on a mass, and the spring moved, the mass moved. But if the spring didn't move, the mass could still be doing something, like pushing back on another lesser mass.

Anonymous

Anonymous Sun 21 Mar 2021 06:59:57 No.12861924 Report

Quoted By:

>>12861223
The limit does not exist at x tending to zero because the function is not continuous anyway. And since the function would be infinity at dx=0 meaning that the slope is infinity = straight line from both sides meaning +infinity and - infinity which makes it clear that dx=0 is not in the domain of this anyway

Anonymous

Anonymous Sun 21 Mar 2021 07:11:45 No.12861951 Report

Quoted By:

>>12861343
are you high

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