Local linearization | Derivative applications | Differential Calculus

Local linearization | Derivative applications | Differential Calculus | Khan Academy

Рет қаралды 540,518

10 жыл бұрын

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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
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Пікірлер: 106

@coolbrotherf127 7 жыл бұрын

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

@shadowvortex6653 10 ай бұрын

exactly

@Flamehara 5 жыл бұрын

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 жыл бұрын

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 жыл бұрын

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

@CyCloNeReactorCore 2 жыл бұрын

👌👌😍 good

@SathickJaffer-hs5sj 8 ай бұрын

In fact, both methods are same

@tianhaosun7131 8 жыл бұрын

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.

@swordfern1052 2 жыл бұрын

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!

@tylerianoakey3738 2 жыл бұрын

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

@ziadhani2738 7 жыл бұрын

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

@Didi-sg8pf 8 жыл бұрын

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

@user-em9mw9ch3y 7 жыл бұрын

congratz bro. invite us to a party now.

@haligali4360 2 жыл бұрын

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

@sindrestokke79 4 жыл бұрын

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

@jeremy6752 5 жыл бұрын

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

@syedrizvi2687 3 жыл бұрын

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

@dilushasiriwardana9642 7 жыл бұрын

Thank you.Perfect explanation..!

@MrEric-rs2wg 3 жыл бұрын

That's actually Mind Blowing

@jun_xg 3 жыл бұрын

very clear, thank you!

@user-dd5jx5nb9e 5 жыл бұрын

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

@ayenewyihune 2 ай бұрын

Super clear!

@anilkumarp8817 6 жыл бұрын

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

@marshelglidden1734 7 жыл бұрын

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.

@david9264 5 жыл бұрын

very helpful, thank you

@Chewychewychoochoo 8 жыл бұрын

Perfect!

@veyselgonel2185 8 жыл бұрын

Very clear lecture, thank you very much.

@bushratarif6028 4 жыл бұрын

Thankyou sir for giving us a great lecture.

@anber4129 5 жыл бұрын

Thank you for this. 😊✌🏽

@xit1254 5 жыл бұрын

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 жыл бұрын

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

@muhammadseyab9032 7 жыл бұрын

thanks khan acedemy carry on you are awesome

@angie337ful 10 жыл бұрын

Thanks!

@jasonbourn29 Жыл бұрын

Thnx

@fernandohipolito4087 7 жыл бұрын

Very cool!

@fahadfaruqi203 3 жыл бұрын

You're amazing khan

@jdtaramona 2 жыл бұрын

Amazing explanation 👏👏👏

@ashik1947 Жыл бұрын

Just amazing 🔥😳

@07ZLeo 7 жыл бұрын

wonderful

@secretpassion3801 5 жыл бұрын

Amazing

@Froggo_kek 2 жыл бұрын

the guy who is talking is very talented at teaching

@FlashTrance 6 жыл бұрын

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).

@xit1254 5 жыл бұрын

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

@nurgulturkmen5508 3 жыл бұрын

wow his voice really reminds me of Corpse's

@its_me5243 4 жыл бұрын

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

@VinsonTran 6 жыл бұрын

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

@JohnSmith-iu3jg 5 жыл бұрын

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

@horrorfilestv 7 ай бұрын

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

@cagataysunal1130 6 жыл бұрын

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

@peneasteca597 6 жыл бұрын

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

@jrwkc 10 жыл бұрын

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

@islulison 10 жыл бұрын

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 жыл бұрын

islulison THANK YOU :D

@tahaanouar2453 7 жыл бұрын

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

@dilli915 6 жыл бұрын

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

@curtis2315 5 жыл бұрын

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 жыл бұрын

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

@azamattf 3 жыл бұрын

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

@FiftiesDad 3 жыл бұрын

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

@footage6402 5 жыл бұрын

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.

@salahuddin2475 3 жыл бұрын

give example of differential equation wich is non linearizable

@arslanrazzaq4982 4 жыл бұрын

anybody tell me the role of linearization in computer science

@samg6046 6 жыл бұрын

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

@sergey_zatsepin 7 жыл бұрын

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 жыл бұрын

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

@mister_allmond 2 жыл бұрын

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

@wabofabo7357 2 ай бұрын

@Ben-sd6ir 11 ай бұрын

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 3 ай бұрын

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

@Ben-sd6ir 3 ай бұрын

@@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.

@ochen222 9 ай бұрын

🐐

@Miloexternalvisions 10 жыл бұрын

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 жыл бұрын

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

@brandondelpesco7329 6 жыл бұрын

At what point is this ineffective??

@Rayalot72 6 жыл бұрын

Probably depends on the graph, and the distance between your known value and the value you are approximating. On a parabola, a tangent line approximating the other side of the parabola is going to be way below/above since you're estimating past a minimum/maximum, as it won't account for the change in slope. Estimating the square root of 50 with the square root of 4 will be a significant difference since the tangent line at x = 4 is going to deviate a lot more once you reach x = 50 than if you are estimating the square root of 5. What are you doing this for? That would probably decide the precision you should be trying to get.

@nigelstanford4 10 жыл бұрын

This is getting into Taylor series

@async7616 7 жыл бұрын

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 6 жыл бұрын

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

@joseguerra225 6 жыл бұрын

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

@david-joeklotz9558 Жыл бұрын

Why wouldn't there be a calculator at hand?

@blocktube1449 5 ай бұрын

Maybe you misplaced yours or can't afford one 😂

@elmarron_17 4 жыл бұрын

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

@user-em9mw9ch3y 7 жыл бұрын

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 2 жыл бұрын

thanks for pointing it out, never noticed it before

@eruiluvatar6688 6 жыл бұрын

Is this not the taylor series?

@where3639 5 жыл бұрын

yes it is a 1st order taylor series

@rileyzheng3318 6 жыл бұрын

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

@hakeemnaa 2 жыл бұрын

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

@kaileejohnson101 3 жыл бұрын

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

@PapaSmurff660 6 жыл бұрын

i hate school

@cariboux2 Жыл бұрын

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

@TritonSeibert 7 жыл бұрын

you really need a pop filter

@BeBold84 7 жыл бұрын

Triton Seibert it's from 2014 lol

@ThirskFrostbane 7 жыл бұрын

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

@animeall3906 7 жыл бұрын

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

@shreeganesh9962 6 жыл бұрын

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

@footage6402 5 жыл бұрын

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

@AristotleFreeman 4 ай бұрын

All a joke.

@stingray1462 10 жыл бұрын

omg, who the hell cares?

@animeall3906 7 жыл бұрын

lol? he helped me alot

@retrogamer9146 6 жыл бұрын

anyone studding for a math test

@SooZoodimp 7 жыл бұрын

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 Жыл бұрын

Thnx