What is linear approximation?

[@ffhashimi]

You spend a lot of time and effort to produce high quality; very informative and useful representations; This is highly appreciated and we thank you for it .

[@DannyOvox3]

Never have I found and Math tutorial with such nice edits.

[@photon2724]

production quality is outta this world!

[@kristakingmath]

Thanks, Photon!

[@mbtisocialclub]

@@kristakingmath you’re welcome

[@cassandratruth]

The sheet I got from my prof explaining this just looked like a giant mess of squiggly lines to me. This broke it down into individually presented little pieces, and was super helpful. Thank you thank you thank you!!

[@kristakingmath]

You're welcome, Cassandra, I'm so glad it helped! :D

[@samcoopermusic]

In addition to the excellent instruction, this video has the music dialed in at very precise levels of volume and funkiness. Thanks Krista King!

[@jquick85]

Keep the vids coming, Krista! I am gearing up for calc 3 here pretty soon and I'll need someone who has great skills with breaking things down!

[@kristakingmath]

I'll be here :)

[@PaintedMessiah]

I was struggling so much to understand this concept. It was like my brain came close to the answer but couldn't get there. You helped me bridge that gap, thank you!

[@kristakingmath]

Awesome, Giorgio! I'm so glad it helped! :D

[@dgd947a15fl]

This is the first of your videos that I've really watched. This one helped me a lot more than other videos on youtube because you take a lot of time to CONCEPTUALIZE it before going into the finer details of the operation. I really liked that. I'm going to go take a look at some more of your videos. If you start off taking a great deal of time conceptualizing things, I suspect I'll find those videos very helpful as well.

[@kristakingmath]

I hope so! :)

[@pbertolini]

Your videos are amazing. The production value makes them extremely watchable and easy to review. You have a real gift as a teacher. Thank you.

[@HotelGenieAI]

I love you, you've changed my life.

[@cariboux2]

Phenomenal explanation! Clear as day. I just watched Khan Academy and was very confused. I came here and within 10 minutes I understood it completely - and realized it's actually just simple common sense - as long as you've got a value really close, which isn't many.

[@krashmans]

I love your videos, they are so easy to understand. Keep it up!

[@mattheModest]

Man. This channel really helped me early on during my studies. I am so happy that it keeps going, I'll keep supporting you with views and likes as often as I can. Thank you.

[@kristakingmath]

Thank you! It's much appreciated. :)

[@nverkhachoyan]

This is amazing! Concise and easy to understand, thank you!

[@kristakingmath]

You're welcome, Nver, I'm so glad you liked it! :)

[@دارالعلومعربیہرجڑ]

Where was this video in 2017 when i needed it desperately.At last i Understand approximation.

[@aaronpicking4935]

Krista, I also have a degree in psychology and have a love for math. So, the use of the Nintendo sounding music in the background is genius! And, the format is as well. Great job in constantly improving your videos.

[@kristakingmath]

Aw thanks Aaron! :)

[@divyanshrai4138]

What does the Nintendo sounding music have to do with it? (genuinely curious, does it make this seem more interesting?)

[@abdurahmanitani5982]

loving these new style videos you're the best krista hands down

[@thesomalistrawhat]

This is good stuff. I appreciate the work you put into making these and I know personally that you make a good teacher. Keep it up, you'll always have at least one avid supporter

[@ash_engineering]

Hello from India, Thank you so much for your efforts and making math so simple to understand .

[@robwhitlock5030]

Delta y, as commonly defined, doesn't give the error in the estimation, it gives the difference between the y values of two points on a function, f(x_2)-f(x_1). The error, on the other hand, would be the difference in y coordinates of two points, one on the function and one on the tangent line, but both with the x coordinate that you are trying to estimate the value of the function at. When you used f(x_2)-f(x_1) = f'(x_1)(x_2-x_1) at 6:47, the form of your equation requires that both (x_1,f(x_1)) and (x_2,f(x_2)) lie on the tangent line of f(x) that touches (x_1,f(x_1)). This is not true for all differentiable functions, and it's certainly not true for the square root function. Note that in your previous equation you had an approximate equality, which was fine, but at 6:47 you changed it to equality, which made it incorrect for most differentiable functions. Finding the value of f'(x_1)(x_2-x_1) doesn't tell you about the error in your estimation, it just tells you how much bigger or smaller your estimate is as compared to where you started, f(x_1). To find the error in your estimation you want to take the difference between your estimate and the true value: true value = f(x_2) estimated value = f(x_1) + f'(x_1)(x_2-x_1) error = (estimated value) - (true value) = f(x_1) + f'(x_1)(x_2-x_1) - f(x_2) Thanks for working to make high quality, easy to understand math videos! :)

[@masumk]

Amazing content! Very simple yet effective explanations. I wish your channel had more subscribers though! You're so underrated!

[@boboganbobogan9297]

After multiple videos you made me understand this, as always

[@kakashisensei3553]

Wow you are so good at teaching math , Loved your voice and presentation skill

[@matheds5043]

Congratulations and thanks for your time producing such videos.

[@sherryk1186]

loving your new editing! thanks for these great videos

[@kristakingmath]

Thanks Sherry!

[@deborahfranza2925]

THIS WAS SUCH AN CONCISE AND AMAZING EXPLANATION OFFICIALLY SUBSCRIBED

[@kristakingmath]

Glad you liked it! :) Thanks for subscribing. 😊

[@calebdodd8381]

KRISTAAAAA....MMWAH FOR THIS ONE..MUCH LOVE

[@mcalioglu]

I actually do love all you videos for they are simple and basic and presented in a smooth step by step fashion... as in this one if I cannot follow them and find them logically false i cannot rely on them... and that makes me sad bec i love you ma'am...

[@Ali-mi9up]

Well explained vids with good quality Keep it up !!

[@kristakingmath]

Thanks, Muhammad! :)

[@gfgarner1301]

Sal Khan (who is a genius) had me going in circles with this. Thanks, Krista, for the clarity.

[@ahmedwaleed6054]

The last formula doesn’t count the value of the error on the linear approximation. It counts an approximation for the change in the function value. It’s specified as an approximation because it uses the linear formula of the tangent line to find the value of the change and the tangent line formula doesn’t represent the formula for the function and the graph.

[@ricric4722]

You're an actual hero!! 😭❤❤

[@TheEathor]

Thank you, your explanations make everything so simple and are lovely too!

[@kristakingmath]

Thanks. :)

[@Jade-kd9ow]

thank you for explaining where the linear approx equation came from I got confused by khan

[@kristakingmath]

You're welcome, Jade, I'm so glad this cleared things up! :)

[@influential7693]

Thank you so much mam for really u have changed my life in many ways 🙏

[@de-grafthazard9081]

I love you Krista😭. Thank you so much

[@kristakingmath]

You're so welcome, I'm so glad the videos are helping!

[@musawalid631]

Excellent explanation 👍 Pleasure

[@sudhar6516]

Thank you!! This helped me very much!

[@kristakingmath]

You're welcome, Sudha! So glad it helped!

[@Billups7Iniesta8C7]

I usually don't comment on videos, but for this one, I had to! Brilliant Job!

[@kristakingmath]

Thank you so much, Mr Gill! :D

[@wealthyboyrr5410]

fantabulous, excellent, simply super, wow... love u r teaching...

[@henrydang5712]

This is so easy to understand. Thank you

[@kristakingmath]

You're welcome, I'm glad you liked it!

[@kambridgecentre3872]

please keep it up.its helpful

[@hibakhatri3076]

this video is AMAZING thank you soooo much for the brilliant video, I really appreciate the effort.

[@kristakingmath]

You're welcome, I'm so glad it helped! :D

[@its703]

By the way your lecture was stunning...

[@astha192]

Greatly appreciate the efforts!!

[@mehlikazeyneparslan3493]

this was sooo helpful! you are a gem

[@kristakingmath]

Thanks, Mehlika, I'm so glad it helped! :D

[@Ridgerunner2270]

Great video like always! Request, could you do a video on liner combinations?

[@kristakingmath]

like this? :) kzbin.info/www/bejne/f2mspp9mhNJgqpY

[@marksami7618]

perfect... just perfect

[@rockyavg7212]

You have earned my loud applause 👏🏼

[@kristakingmath]

Aww thanks! :)

[@harishakthikarthikchokkana4864]

Thank u so much for this lesson

[@kristakingmath]

You're welcome, Hari! :)

[@anuragjain4474]

Hi Krista, just saw your tutorial. It's amazing. The creative way by which you were passing over this information is fantastic. But I have certain problems with your notations, don't you think linear approximation is more precise word you should use instead of linear interpolation as by interpolation we mean to find approximate function in a given range when we have information about function in that range. You aren't really using any range here, you are using information at a point to find information on another point. Second point is when you calculated error, how can that be an error?

[@billygraham5589]

Good, but I don't get the "error" part. How can you come up with an error factor when you are using an equation to calculate the error which was a (linear) estimate for which we don't really know the error? As I see it, the only way to determine the "error" is to use a calculator an determine the actual value of f(x) at the "difficult to calculate" point. And if I could do that why do a "linear approximation?"

[@madhavanand756]

This is wonderful

[@kristakingmath]

Thanks, Madhav! :D

[@rocketkinger2506]

love the video quality

[@programinggrid967]

This video was very helpfull to me

[@kristakingmath]

I'm so glad it helped! :)

[@deveneb8409]

so basically if you dont have a calculator then its useful?

[@ResearchandThink]

Great video!

[@sagargurung8682]

Please do some videos on PROBABILITY...

[@clairieberry9558]

Thank you so much!

[@kristakingmath]

You're welcome, Clairie! :)

[@karansaini305]

excellent technique to teach

[@kristakingmath]

:D

[@rbjassoc6]

Love the video but I am missing the jump from understanding why pi/3 is close to 1.05 ??? ( 5:41 ) how do I know that ??

[@puddingninja]

π ~ 3.14; 1.05=n*π; n=(1.05/3.14); n=(1.05/3.14) ~ (1/3); n*π=1.05=(π/3);

[@astha192]

understood the concept!!!

[@roa1437]

LIFE SAVER

[@mcalioglu]

hello dear ms. krista king, in this video what you call an error and what you calculate for error is not the exact difference between the real value of f(1.05) and the approximated number found for f(1.05)... are we clear about this ma'am...

[@altheacastro5543]

i love you krista,, i really do

[@isaacmarzuca680]

Hey Krista, just wondering if you could please explain how you got "1/8" when doing (1/2)16^-1/2. I tried putting it into calculators numerous times but I can't figure out how you solved it.

[@DanT-iu6oc]

KK, you explained this better in 9 minutes than a 200 dollar textbook and a college professor paid 200k/year at my local college. You are living proof that math education needs to modernize itself. James Stewart's textbook is damn garbage.

[@kristakingmath]

I'm just happy to help! :)

[@ashw730]

Thank s for the video. I dont understand the cos(x). Can you pls simplify cos x with y-y1=m(x-x1)

[@betht840]

f(1.05)-f(1.0467)=f'(1.0467)(1.05-1.0467) Where ... 1.0467 is 'pi/3' and f'(1.0467) is 'm'

[@aminmoafi5148]

🙌 bravo!

[@prestonsso12]

WOW, i have your udemy courses, i didn't know you were on youtube as well. nice

[@huntingtonco8379]

Thank you

[@AlexDonnett]

I got a B in calculus last semester when I thought for sure I would get a C. THANKS

[@kristakingmath]

That's awesome! Congrats!

[@happybird2621]

Thank you very much

[@kristakingmath]

You're very welcome! :D

[@bishalpoudel481]

hey kristia can u please make videos related to simplex method...

[@xiaoyuhu7446]

Great sense ! BTW Whats the BGM? xD

[@H0peAnL0ve]

thank you so much, my textbook was making no sense

[@kristakingmath]

I'm so glad this helped clarify! :D

[@abdelz1617]

very helpful

[@kristakingmath]

Glad to hear that, Abdel! :)

[@its703]

But we can find this by using a calculator... Then why is this method useful?

[@all_mesa_man922]

Oh it's you again! I was like "man why can't my Calc professor just hire this person?" I also said that in the first of your videos I ever watched. I just didn't recognize your voice this time! Thank you for taking the time to help us. I am taking entry level advanced math for the first time in life at nearly 30 years old and it's kicking my ass up and down the street. Thanks Krista!!! I might actually pass Applied Ordinary Differential Equations when I have to take it in 2 years!!

[@kristakingmath]

You will _absolutely_ pass ODEs, you've got this! I hope I can help all along the way! :D

[@hg2.]

Hi Krista, this presentation style too fast - it glosses over one of your strongest teaching talents, which is your narrative attention to detail as you are writing the material down - that way your excellent spoken narrative is "in synch" with the formulas as they are being written down.

[@hg2.]

This makes me appreciate the literally 100s of videos you've made in the "Classic Krista style".

[@hg2.]

+hettygreene ... and sorry, but the background music is just simply distracting.

[@kristakingmath]

Thanks for the feedback! As I'm sure you've noticed, I've been trying tall different kinds of things for fun. :)

[@antruong1575]

love her voice :))

[@biswajitbaruah8974]

Your thumbnail posses are out of world 🤣😂

[@IntensePeppers]

First video I've ever seen of yours, nice job. But you look like a prison inmate in the thumbnail haha

[@kristakingmath]

😂

[@marksami7618]

perfect.....

[@sriramsaikrishna1874]

Super 😍

[@astha192]

Nd ... excellent voice!!

[@noahgsolomon]

Goat

[@arj123sub]

Awesome

[@juraijbinjamal5313]

Was that background music necessary?!!!

[@oppongedmond7918]

Good! But too fast for a slow learner like me

[@CesarAHaro]

The music didn't let me focus

[@marksami7618]

👌👌👌👌👌👌👌

[@ClumpypooCP]

interesting

[@johnstillman2935]

would have been better without distracting music !

[@mettataurr]

i love you

[@sarahyummers]

Has anyone else noticed that the background music sounds like Animal Crossing music? XD

[@susienajaryan9006]

@1:27 because we can get the better answer quicker with a calculator lol

[@_DD_15]

4:53 don't do this pleaseeee :( what about the derivative definition and all the crap. The limit has to be finite and the function continuous. we want precision :)

[@PRod745]

Just marry me!

[@jiwonchang1470]

do you like doge