Local linearization | Derivative applications | Differential Calculus | Khan Academy

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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
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Опубликовано:

8 окт 2024

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Комментарии : 108

@coolbrotherf127 8 лет назад

This was a lot better than how my teacher explained it. I was so confused, but this helped a lot.

@shadowvortex6653 Год назад

exactly

@Flamehara 5 лет назад

I've found that using point-slope form to find what you called L(X) made my final approximation a lot easier. After making an equation in this form (y-y1)=m(x-x1). Our y1 in this case was 2 and our x1 was 4. We find our m/slope with the good old power rule of the original equation to get 1/4. Our point-slope formula is now complete, reading Y-2=1/4(X-4). you simply plug in your new value (which in this case was 4.36) for X: Y-2=1/4(4.36-4). Solve for Y and you get 2.09!

@Flamehara 5 лет назад

our Y1 and X1 were the coordinates of the point of the intersection of the tangent and the function. Hope this helps someone!

@mrgreen5060 2 года назад

Head the same idea...a simple point slope form

@CyCloNeReactorCore 2 года назад

👌👌😍 good

@SathickJaffer-hs5sj 10 месяцев назад

In fact, both methods are same

@gamingguy3363 3 дня назад

This did help a ton. Thanks, I was struggling to wrap my head around the other method, this just feels more intuitive.

@swordfern1052 2 года назад

It's incredible that my teacher hands us spreadsheets and tells us to learn, while with this we're shown every step and are given an explanation on what's happening. Thanks!

@tianhaosun7131 8 лет назад

I like how i got a math tutor ad on a khan academy video, I thought youtube had a good ad algorith. Khan for life.

@tylerianoakey3738 2 года назад

Hi Professor, just wanted to say how much I enjoy your teaching abilities. Thanks for the fantastic videos.

@Didi-sg8pf 8 лет назад

Thank you for helping me get a 100% on my calculus final!!!!

@user-em9mw9ch3y 7 лет назад

congratz bro. invite us to a party now.

@jeremy6752 6 лет назад

this is so much clearer than my math lesson at university !!

@marshelglidden1734 8 лет назад

Hey Sal, just so you know, you can usually hold the ctrl key and use the scroll wheel to change the zoom on the current screen. Might be worth a shot later on.

@ziadhani2738 7 лет назад

Thanks for the videos. You helped a lot of people to understand things in Calculus.

@haligali4360 3 года назад

Man, you're amazing! I hope you're good in 2021!

@xit1254 6 лет назад

The way you came up with the line equation confused me a little. It was clearer to me when I put it in slope-intercept form: (F(x) - F(4))/(x-4) = F'(4) and solving for F of x gives: F(x) = F'(4) (x-4) + F(4)

@mister_allmond 2 года назад

yeah i'm not sure why he just wrote that equation without explaining anything about it.

@veyselgonel2185 8 лет назад

Very clear lecture, thank you very much.

@MrEric-rs2wg 3 года назад

That's actually Mind Blowing

@Froggo_kek 2 года назад

the guy who is talking is very talented at teaching

@sindrestokke79 5 лет назад

Thank you so much, I wouldn't have understood this without this great video!

@syedrizvi2687 3 года назад

THANK YOU! :D Khan Academy is such an amazing tool!

@ayenewyihune 4 месяца назад

Super clear!

@jasonbourn29 Год назад

Thnx

@fahadfaruqi203 3 года назад

You're amazing khan

@anilkumarp8817 6 лет назад

thank you sir for your help.and we are expecting more from you

@jun_xg 3 года назад

very clear, thank you!

@dilushasiriwardana9642 7 лет назад

Thank you.Perfect explanation..!

@david9264 5 лет назад

very helpful, thank you

@ashik1947 2 года назад

Just amazing 🔥😳

@VinsonTran 7 лет назад

Essentially the formula used is f(a)+f'(a)(x-a) then plug and chug

@JohnSmith-iu3jg 5 лет назад

Vinson Tran which itself is in the form of y=mx+b (actually it's y=b+m(x-c))

@FlashTrance 6 лет назад

Thanks for these videos, but fyi this one is out of order and very confusing in a couple parts. I didn't understand the derivative power rule at all (because we haven't yet learned it if we're watching in order) and was completely confused about how you "randomly" found out that f'(x) was 1/2x^-1/2. I think the fact that you were using a re-arranged point-slope form for L(x) should also have been stated from the get-go. I ended up giving up on your equation for a while and found the same answer using mx+b and the value of 1/4 given for f'(4) (slope-intercept form is what was used in an earlier video as a method for finding a tangent line equation).

@bushratarif6028 4 года назад

Thankyou sir for giving us a great lecture.

@jdtaramona 2 года назад

Amazing explanation 👏👏👏

@muhammadseyab9032 7 лет назад

thanks khan acedemy carry on you are awesome

@angie337ful 10 лет назад

Thanks!

@신명은-r2d 5 лет назад

Thank you for perfect explanation. Your writing was clear, so I could understand more.^^

@nurgulturkmen5508 3 года назад

wow his voice really reminds me of Corpse's

@anber4129 5 лет назад

Thank you for this. 😊✌🏽

@Chewychewychoochoo 8 лет назад

Perfect!

@fernandohipolito4087 7 лет назад

Very cool!

@horrorfilestv 9 месяцев назад

you could just use point slope form rather than that other form for L(x)

@xit1254 6 лет назад

At 6:02 you said the change in x is 4.36. Shouldn't that be 0.36?

@salahuddin2475 3 года назад

give example of differential equation wich is non linearizable

@jrwkc 10 лет назад

i don't get how the equation of the L(X) was formed.

@islulison 10 лет назад

The equation is derived from the alternate definition of a derivative f(b)-f(a) / (b-a) = f'(c) The equation simplifies to f(b) - f(a) = f'(c)(b-a) and then to f(b) = f'(c)(b-a) + f(a). (When writing the final form of the equation c = a) So you get: L(x) = f'(a)(x-a) + f(a). x is the number you are trying to estimate for. a is the number that has a known value f(a). if you have an equation for f(a) you can find the derivative and plug in a. multiply that by the difference of x and a (x-a) and then add the value of f(a). you will get L(x) which is really f(b) from the original derivation. This value is close to what the actual value should be so you can use a calculator to determine if you did it correctly or not.

@vancouvercanuck4life 10 лет назад

islulison THANK YOU :D

@tahaanouar2453 7 лет назад

+MahNimbus that's what I was searching for ... thank you so much ^^

@dilli915 6 лет назад

hey ,pleaase how is 4^-1/2 = 1/2?

@curtis2315 6 лет назад

Because 4^-1/2 can be rewritten as 1/(4^1/2). 4^1/2 is equal to 2. Thus 1/(4^1/2) is equal to 1/2.

@kijix85 6 лет назад

6:00 sorry confused. you said its 4.36 away from X .. don't you mean its .36 away from X?

@azamattf 3 года назад

Have the same question. But he said "Change in X is 4.36". I think he meant "Change in X is 0.36"

@secretpassion3801 5 лет назад

Amazing

@its_me5243 4 года назад

Can every function be linearized ? If not give a counter example

@07ZLeo 7 лет назад

wonderful

@wabofabo7357 4 месяца назад

@sergey_zatsepin 7 лет назад

Well, it's unclear for me why the equation for this tangent line is f(4)+f'(4)(x-4), from where we get it?

@ary480 4 года назад

Sergey Zatsepin That’s the equation y-y0=m(x-x0)

@mister_allmond 2 года назад

@@ary480 yeah i'm so confused as to why Sal just assumed everyone would realize that?

@FiftiesDad 3 года назад

great videos. i noticed that i noticed that you repeat yourself a lot

@hakeemnaa 2 года назад

easy slop is 1/2sqr4 =1/4 y=mx+c y=1/4x+c but you know you have a point on it (2,4) so c=2-1/4*4=1 so the line equation is y=1/4x+1 then y=1/4* 4.36+1 =1.09+1=2.09

@cagataysunal1130 7 лет назад

So it is basically the function of the tangent line eh? Just really close

@footage6402 6 лет назад

Why do this when there is newton's method? squrt of 4.36 is just doing x^2 -4.36 then finding the root using newton's method.

@peneasteca597 6 лет назад

Are there any other methods? Maybe one that is more accurate?

@Ben-sd6ir Год назад

Does the original 'x' value (the 4 in this video) need to be close in value to the x you are using to find L(x) or can it be any amount you already know the f(x) of?

@TU7OV 5 месяцев назад

Can be any but the approximation will be way off if the difference between x and a is huge.

@Ben-sd6ir 5 месяцев назад

@@TU7OV recapping this video makes more sense now than it did back then. That makes sense, I suppose it's because the difference or factor would increase and negate the original value that you're trying to find the function of.

@samg6046 6 лет назад

the way in which you described L(x) was very unclear, you didn't find the equation of the tangent first, instead you subbed a function of what y of the point would be which is misleading unless you already understand this. otherwise the video was helpful

@Miloexternalvisions 10 лет назад

Is he actually writing all of this with his mouse? If he is then that's awesome. If not , can you guys tell me how he's doing it?

@MP9220 10 лет назад

He's using a draw pad or whatever you call them.

@arslanrazzaq4982 5 лет назад

anybody tell me the role of linearization in computer science

@brandondelpesco7329 7 лет назад

At what point is this ineffective??

@nigelstanford4 10 лет назад

This is getting into Taylor series

@async7616 7 лет назад

why don't you just form the equation of the tangent line and just substitute the x-value of the other point(4.36) ...... you still get the correct answer...

@michaelfjmusic 7 лет назад

It's because this method can be used to approximate square roots without a calculator.

@joseguerra225 6 лет назад

If we knew the value of the sqrt of 4.36 without a calculator, we wouldn't need this in the first place.

@kaileejohnson101 3 года назад

face reveal !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

@ochen222 11 месяцев назад

🐐

@rileyzheng3318 6 лет назад

I just want to know who’s quiz will be this easy???

@david-joeklotz9558 Год назад

Why wouldn't there be a calculator at hand?

@user-em9mw9ch3y 7 лет назад

I have watched your videos so many times and each time, the idea that an 'Index finger' writes all these stuffs, makes me cringe.

@sonny1524 3 года назад

thanks for pointing it out, never noticed it before

@elmarron_17 4 года назад

How did you know that 1/4 × 0.36=0.09 Without using a calculator?😏

@mirilondondrift 8 дней назад

you couldnt just do y=mx+c? this is just overcomplicating things

@eruiluvatar6688 6 лет назад

Is this not the taylor series?

@where3639 6 лет назад

yes it is a 1st order taylor series

@PapaSmurff660 6 лет назад

i hate school

@cariboux2 Год назад

I'm missing something, because this makes absolutely no sense to me.

@TritonSeibert 7 лет назад

you really need a pop filter

@BeBold84 7 лет назад

Triton Seibert it's from 2014 lol

@ThirskFrostbane 8 лет назад

I feel like this video would be a lot more informative if a more confident speaker recorded it.

@animeall3906 7 лет назад

this guy seems pretty confident and i like his deep voice , just makes me in the zone to study

@shreeganesh9962 6 лет назад

3Blue1Brown guy is better than Sal. This video is done by Sal

@footage6402 6 лет назад

@@shreeganesh99623blue1brown voice is nerdy af though. Plus Sal is the best teacher online.

@AristotleFreeman 6 месяцев назад

All a joke.

@stingray1462 10 лет назад

omg, who the hell cares?

@animeall3906 7 лет назад

lol? he helped me alot

@retrogamer9146 6 лет назад

anyone studding for a math test

@SooZoodimp 7 лет назад

5:40 I am not sure about the number 2 in [4.36; 2 + f'(4)*0.36] L(x) = f(4) + ... I see that f(4) = 2 ... but if we are talking about a x=4.36 ... shouldn't there be f(4.36) instead? Of course we doesn't know that value yet ... I just want it to be clarified ... I understand it the way .. that we have to use f(4) exactly for the reason, that we don't know f(4.36) yet ... am i right?

@jasonbourn29 Год назад

Thnx