Explain limits to me

This

Why are limits so much harder to understand than infinitesimals?
Everything makes sense when I use (f(x+h)-f(x)) / h for derivative function and iterated trapezoid for integral function, but then for some inexplicable reason a bunch of mathematicians from a hundred years ago decided to invent some retarded limit bullshit just to confuse me.

And to add to this, what the fuck is with that extra arrow notation and how do you know which numbers to even choose as your limit out of the function and is there some simple deterministic way to get the right answer the same simple deterministic way you can write in an (f(x+h)-f(X)) / h method with h set to some arbitrarily small number and just call it whenever you want your program to do numerical differentiation?

They are the only value of a function said function will never reach as it approaches a given x value

Analysis isn't real math

en.wikipedia.org/wiki/Limit_(mathematics)

it can't be explained. either you are a retarded nigger or you aren't.
i can only tell you how to understand it.
read the explanation in the chapter again. read it again. then read it again before you go to sleep tonight.
if you wake up in the morning and you still don't understand it, switch to gender studies tomorrow.

btw it's a bit late in the semester to be asking this. chances are you are 100% brainlet.

KEK
E
K

KEK all you want but think about what OP is struggling to understand.
"what is the output of [math]f[/math] as we input values approaching infinitesimally close to x?"
there is no simpler way to put this.
guarantee his professor even has drawn graphs up and had them calculate 0.9, 0.99, 0.999, 0.9999... clearly illustrating the point.
IF you need more help than that.. i know it's uncomfortable to admit but.. well...

The "Y" as x approaches a certain value, is ... for example the limit as x approaches 2 from the function 2x is 4. The limit is at 4. There's also the whole deal with one sided functions and such but what I just explained are the basics

The strongest explanation is to calculate F(x)=2x at x=1.9
then x=1.99
then x=1.999
then x=1.9999
then x=1.99999

then you ask: what does F look like it's going to be as x gets ever closer and closer to 2?

At this point, negroid brains will flip out or go into a sense of disbelief. You can do nothing to help them, trust me.

look up delta epsilon definition to limits

can you post the vid or article where they discuss why this definition is problematic?

Infinitesimals are a spook

Instead of studying what a function equals at a point you study what values the function takes close to that point.

Limits are simply the modern and accepted formalization of this idea, but any intuitive approach would be good enough for a beginner. And any definition you could come up with to make it formal will probably be as good or at Cauchy's, at least for a simple exploration.

Something annoying that you have to keep track of until you finally plug it in. god forbid you have to apply l'hopitals rule

The limit of a function f at the point x0 is y0 means that for all sequences (xn) in the domain of f, lim xn = x0 implies lim f(xn) = y0 I think.

No means no.

What is there to not understand, brainlet?

>t. I don't understand the intermediate value theorem
"No"
There's no problem. You just slide through a point that must be there without going there.

Perhaps you need to visualize it more, either way there's multiple ways to ingest this. I suggest you start looking at each and keep doing so until it clicks. You can see the equations written down, you can use examples from that written down, you can see graphs, you can see videos. Something in nature can be used to help this out as an analogy.

This is a troll thread, but I'm sure some people might happen upon it and wonder. I haven't seen this shit in ages I forgot as well.

user I'm black and you're right. I speak perfect English, but...
>then you ask: what does F look like it's going to be as x gets ever closer and closer to 2?
Those words. It must be witchcraft. Those must be magical words, and you've cast a spell on me. I immediately became perplexed the first time I read them, then I tried reading those words a second time, third time, a fourth time, and I don't know what number comes after 4 but I still couldn't understand anything. I became increasingly distressed and anxious, my palms became sweaty and my hands shook uncontrollably. Those words filled my vision, a shiver went down my spine and I felt panic and adrenaline rushing into my veins. My entire being and soul were overcome by primal fear and anguish, I jumped from my seat and began beating my chest and hooting and hollering. I don't know what the fuck just happened. Calculus is clearly some evil white magic used to enslave and corrupt the very forces of nature. Shiiieeet

In layman's terms; the limit of f(x) when x approaches a is the value f(a) would have if we assume f to be continuous. Go to Khan Academy or 3Blue1Brown.
If you're talking about the rigorous definition of limits, then the limit of f(x) as x approaches a is the limit point of f(A) where A is the set of all limit points of a. Kinda. Can't help you if you don't know a little bit about the topology of the reals. Read an analysis textbook that has a topology section.

Sidestepping maths paradox including dividing by zero by putting everything in a neat place then diving by 0.

>Everything makes sense when I use (f(x+h)-f(x)) / h for derivative function
That is the limit definition! The infinitesimal definition replaces h with dx, which is treated as always being infinitely small instead of treating h as finite and taking the h->0 limit.
I don't understand the question. In the case of the derivative there's only one limit, the h->0 one. If you take take multiple derivatives then the first derivative you calculate is the first one you take the limit for. Your "setting h to some arbitrarily small number" is just a non-rigorous definition of a limit, it is no more deterministic than the rigorous definition.

Suppose you were tasked with running a race.

However, you are mentally retarded and can only run distances in bursts. In each burst, you will run half of the remaining distance.

Lets say that the race you have to run is L long. That is to say, you will start at distance d = 0 and be completed at distance d = L.

I'm an onlooker to the race realizing how retarded you are. I turn to my friend and say "Hey, I bet he will never reach ε feet of the the finish line d = L,!"

My friend responds "Actually, you're wrong. He will reach ε feet of the finish line at time s = 𝛿! In fact, for ANY ε feet from the finish line you give me, I can give you a time 𝛿 where he gets at least that close!"

Realizing I was wrong, and that despite never reaching L, you will get arbitrarily close to it. Therefore, I conclude that L is the limit of the function of you running the race.

Best and only good response so far

>can't apply it for anything converging asymptotically slower than 1/n
>non-problematic
Your baits need to be more subtle, user.

This.

Have a sequence. Put a box around a certain value. Can you find a term in the sequence beyond which the value of the sequence will always be in the box? It doesn't matter what it does before that point or how much it moves around in the box as long as it's in the box. If the answer is yes, how small can you make the box? If you can tighten it as much as you want around a certain point, that's the limit.

y= x
what happen when x reach to 4? y becomes 4
y=1/x
what happen when x reach to 0.0001? y gets a real big number,it is so big that you can call it infinite
what happen when x reach = lim x->value (4 or 0.0001)

damn thats the boring explanation
but it is correct

That's a good explanation.

>Give epsilon which requires a delta past physiological collapse
Wasn't so hard

now explain epsilon delta definition

Your brain has limits.

Can you eat whole pie by always cutting only half of it?

ther
ar
no
limts!!!

> Explain limits

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Uhuh Uhuh.

Suppose you have a curve, a function, and want to find the straight line tangent to it at a particular point. Call that point A.
Take that point and a nearby point, B, on the curve. Slope is defined as Rise (the Y distance between the points) divided by the Run (the X distance between the points.
To find the slope at A, you move B closer and closer to A. At each location you compute the tangent. If the point is "well behaved" (there's not an abrupt kink or discontinuity at A) then the slope settles down to a constant value.

But if B moves right _to_ A, their X-separation is zero and you're not allowed to divide by zero.
So you imagine A and B are still separated by dX, a very very very small quantity.

If it's any consolation, it took centuries for mathematicians to put Limits on a firm footing and replace the hand-waving Newton and Leibnitz employed.

>problems without exact solutions

those don't exist unless you activate Godels almonds, brainlet

youtu.be/XFDM1ip5HdU
watch this, and then maybe watch it again

Is there a (good) way to define a tangent line without using limits?

yes

ask isac nuton

fpbp

Yes

Theory saying were able to lift cars if not jumbo yets. It's the minds way of telling you knock off being too strong is not successful. It's the same as ants carrying 30 times it's weight. We humans are born very futile. So complex machinery need time to nurture properly. Theres no way around, or is it? You see shaolin monks are bending and streching laws of nature. Moving energy and such. One could basically become bulletproof if fully mastered. That's kinda cool stuff.

"A straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point."

WTF does this have to do with the topic?

Incidentally, I've never seen Shaolin monks (or anybody else) bending or stretching the laws of nature.
I _have_ seen tribal warriors & guerillas advancing into machine gun fire, confident of "spiritual" protection.
They were dead in the next instant.

It's entirely possible to pass Calc 1 by treating limits as just any other variable because you don't understand what they are. I didn't get limits until early November and finished the class with a middling B because you just treat x --> 0 as 0