Limits?

A limit in the lamest of terms is "this pool of suggested numbers are as close to this number as possible but aren't this number". With the limit being the basic idea of that suggested pool of numbers.

lol baited

how the hell do you go from the 1st line to the 2nd line?

The function you're differentiating is y=x^2. Have you taken grade 10 calculus...?

It's just written oddly faggot

Tbh, most people don't see limits or derivatives in hs. Just saying

the parts where you see an x... you write x + h instead, thus f ( x + h) instead of f ( x )

kek

And you couldn't figure it out? Honestly, you're the reason Veeky Forums is going to shit. Please wait until you're in uni to post more

grades don't measure intelligence, they measure obedience.

Let f be a function defined on an open interval containing a except perhaps a itself. Then we say the limit of f(x) as x approaches a is L if for every real number epsilon > 0 there is a number delta > 0 such that if 0 < |x - a| < delta, then |f(x) - L| < epsilon. You're welcome, young nigger, please do something worthwhile with this knowledge instead of becoming a wizard like me.

The limit of f(x) as x approaches c is basically a value that you can get f(x) as close to as you want by getting x close enough to c, even if f(x) never actually reaches its limit or you can't have x=c.

the limit does not exist

youtube.com/watch?v=-ejyeII0i5c

youtube.com/watch?v=Fdu5-aNJTzU

watch them in order young fagling.

For some function [math] f:\mathbb{R}\rightarrow \mathbb{R}[/math], then the limit as x approaches a of f(x) is said to exist and equal $f(a)$, that is [math] \lim\limits_{x \rightarrow a} f(x) = f(a) [/math], if

[math] \forall \ \varepsilon>0, \ |x-a|

>current year
>not using varepsilon

ignore the $ around f(a), slipped through the cracks.

>using the word derive
>telling other people to go back to high school
ISHYGDDT

At least add in "not using differentiate" or something so that people know what they should say.

>Badly defining continuity
>Not instead defining uniform continuity
>Not defining uniform continuity more generally in terms of functions on metric spaces
ISHYGDDT #1

>Using a epsilon-delta limit definition to help the OP who can't even understand his image
>Taking first analysis course and waving e-peen this hard
ISHYGDDT #2

>"What it means is that for all ε>0, then I can make x arbitrarily close to a (but not equal to a), such that |f(x)-f(a)| is strictly less than ε, but because this is true for all ε>0, then I can make f(x) and f(a) infinitesimally* close to each other."
>Taking the time to write your crappy definition again but just substituting symbols with words, making even less sense, and being flat out wrong
ISHYGDDT #3

>"If you can't quite understand this then go read some analysis books, start with sequences, then series, then functions."
>Telling the OP to read stuff he doesn't need to know to understand the limit definition at his level
>Implying you've read any serious analysis book and know what's in it
ISHYGDDT #4

>"A derivative is basically [insert incomplete textbook definition here]"

>American education system

sure, homie. keep telling yourself that while you are regaded as average by everyone.

grades show how much effort you put into what you were supposed to do, and indirectly indicate intelligence because the intelligent person will work harder in school.

besides university isn't even hard. it's just a lot of work. anyway, you'll have to live with these choices for the rest of your life, not me.

Well done op, nice bait.

>What the fuck is a limit
• found the "D" student
• enjoy your career in the food-service industry
• no, I don't want fries with that...
• ...if I wanted fries, I would have said "fries"

> obedient brainlet detected

Im not from merica and i just learned this shit in my frist year of college/university

Where are you from then? As far as I know, all of Yurop and Aus learn calc in highschool

Third World countries (south merica)

I think is not necessary to learn that shit in highschool, like you will never use that, unless you get in college

where from, nigger?
Argentina here. i had to learn this in the 4th year, but education literally failed me. in college it was easy tho

OP is not going to know what those Greek letters represent in the epsilon delta definition you posted.

>thinks he wasn't the one who got baited

People who call college uni are such pretentious faggots I swear to god

This guy has autism

>People who don't live in burgerland are such pretentious faggots

shiggity

It's people trying to gloat about being at a 4 year school rather than starting a 2 year school.

Okay well in canada everyone goes to a 4 year school (unless you're doing a trade or something) and they call it uni. The only people who call it college are students from america.

>mfw most Americans learn this for the first time at the age of 18
>mfw my country had me doing real analysis at 18

heh, tough luck, brainlets.

uniform continuity isn't needed here you fucking undergrad brainlet

>waving e-peen this hard

said the guy who ask someone to define uniform continuity on metric spaces for someone trying to explain limits XDDD

absolutely kill yourself sub-human cs student lm*ao@urlife

>Doing real analysis in first year
>High school doesn't teach real analysis to seniors

LMAO are you from a third world country?

>implying i said uniform continuity is "needed"
>"said the guy who ask someone to define uniform continuity on metric spaces"
what is reading comprehension

>responding to bait responses

ISHYGDDT #5

He actually didn't specify f =x^2 before starting the differentiation.

ITT I know calculus look at how smart I am

That goes for you "analysis"fags too.

The worst people on sci are the ones who took calc in high school with a little point set topology and say they have taken analysis. Unless you have completed baby Rudin you haven't studied any analysis

>derive

Retard.

and then Americans will catch up anyway, because their unis are world-class.

Nice work, brainlet.

>Thinks he can see where the baiters end

what is a rope

find one and neck yourself dog

>calc in high school with a little point set topology

That is literally Rudin.

He is right though faggot

youtube.com/watch?v=Vv1BUCkgsr8

I think he's talking about papa rudin.

Someone can correct me if I'm wrong, and continue to rash me but if I were to explain it.

I'm sure by now you've learned about approximating the slop of a point by finding the secant line.

That is, you have point x, f(x). x representing the value on the x axis, and f(x) representing the value on the y axis.

The other point (since you have secant line) can be considered to be x+h, f(x+h). h how far the second point is from the first point.

for example, we have a point with an x value of 1 and a second point with an x value of 5. h would be 4. (1+ h = 5)

So now we have the two points (x,f(x)) and ((x+h),f(x+h)). Using the slope formula y2-y1/x2-x1 we end up with.

(f(x+h) - f(x))/h

Now incorporating limits, our goal is to minimize the gap between x and x+h infinitely. This will get us the most accurate slope at that point. So we take the Limit at h approaches 0, of (f(x+h) - f(x))/h.

I'm also only taking calculus for the first time so take everything I say with a grain of salt.

Line 5,
>>h how far the second point is from the first point.

h isn't how far the second point is from the first point.

[f(x+h)-f(x)]/[(x+h)-(x)] is how far the first point is from the second point. h is just the delta x in this case.

Otherwise your laymen explanation is correct.

Shit you're right, my bad. Thanks for correcting me.

I'm not sure if this thread is bait, but if it's not I understand where the guy/girl is coming from. At least in my High School (the united states) they kind of just throw the equations at you without giving a "why".

>Unless you have completed baby Rudin you haven't studied any analysis

Nah, he straight up says baby Rudin.

>tfw someone who hasn't even read baby Rudin himself tells other people that they haven't taken analysis unless they have read baby Rudin

J
U
S
T

It might be bait it might not be. The worst part is it's one of the more interesting math related threads going on right now so I have literally 0 problem with it.

That's too bad, mathematics is supposed to be all about the "Why".

it's pretty much implied from the second line.
>when you need everything explicitly stating from the start you're not a math student but an expensive and high maintenance version of matlab

True, but as a TA for calc 2 the purpose of real hooman beans is not to be calculators anyways. The purpose is to learn and then maybe apply concepts learned or if anything learn it well enough so I can hand you marks on a test.

hooman != compooter, senpai.

>high school

I wish I was as young and dumb as you are.

Probably gonna post the simplest solution here knowing how complicated Veeky Forums can be. So we know the derivative of a function is the slope at any point, right? What is the equation for slope? Rise over run, right? y/x. Look at the limit. We have f(x+h)-f(x) meaning at some x value h after x we take that y-value and subtract the y-value h xs ago. We then of course divide that by the x (h)! The limit is to obtain the precise slope at a point as x gets smaller and smaller.

This board is absolute banter. Seriously, can only fucking grad students or above post on here without getting shit on? I should just pretend I'm a professor and call you a postdoc brainlet retard

learn what limits are and why we use them before starting differentiation, otherwise youll end up like one of those chinks that knows how to do everything when told, but is lost when trying to figure out something for themselves.

Don't come back till you throw some L'Hôpitals at it. It'll be fine; I'll be back when I finish Lebesgue Integrations.

mate, you're never gonna cut it in real math

>being this tilted after getting five shiggy diggies and having your post called bait
[eqn]l \circ l[/eqn]

>Than go back to high school
>Than
Take a look in the mirror bud

What property is that?

I'm average. I got good grades in high school.
>I bullshitted essays
>I was good at eliminating multiple choice options
>I sucked up to the right teachers
>I was good at following directions

I'm in a top 20 American university with already a semester's worth of AP credit, but I'll be the first to tell you I'm not intelligent. My English essays involved so much BS they were basically handwritten shitposts. Math is the most basic shit in high school, and anything I didn't understand the teacher would explain to me like I was slow (hint: I was). High school grades are a fucking meme, and undergrad seems the same. It literally is a measure of how good you are at gaming the education system, and has only a small correlation to actual intelligence.

Pic related, """science""" in high school is literally just memorizing flashcard stacks of names and shit. Zero brainpower required, a fucking monkey could """learn""" this after enough time.

>He will always be a brainlet stuck in a professor job
>He will never know the feeling of actual intelligence
>His highest dream will be to achieve tenure

A limit defines a value n as a value of f(x) as x approaches infinitesimally close to a. Limits are useful to define values that would otherwise be undefined by the function f(x), such as for asymptotic functions.

Differentiation is basically evaluating the instantaneous rate of change f'(x) at x. Define x+h as a value that is infinitesimally close to x. The straight-line slope between f(x) and f(x+h) is the value of f'(x). The slope f'(x) is just f(x+h)-f(x)/((x+h)-x) = f(x+h)-f(x)/h. Since we need to evaluate with x+h that is infinitesimally close to x, we can evaluate f(x+h)-f(x)/h using a limit where h approaches 0, since h must be infinitesimally small (h being close to, but not equal to zero).

t. idiot whose highest level of mathematics education is first year undergrad (which is basically the same as high school graduate)

...

Well sure, you don't have to learn it, but if you're not a brainlet you won't take shit maths

>infinitesimally
stopped reading there
nice dubs

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