Finding the Linearization at a Point / Tangent Line Approximation 

I spread the word about your site like crazy at my school... I call you the Math GOD! Thank you for showing me the light. Keep these videos up here forever I promise when I graduate BECAUSE of you I am going to donate a lot of money to your site... Truely talented my friend

I LOVE YOU. My final exam is tomorrow, and I had NO IDEA how to do this. I LOVE YOU. I LOVE YOU. I LOVE YOU. Please don't ever go away.

This video make me realize that right handed people are better for this, because their hand doesn't cover up everything as they are writing.

Thanks, my teacher is an idiot but these are SO much more helpful, it's like having a personal teacher

i am so glad that you take the time to explain a subject like this through videos it makes understanding calculus so much easier

0:57 you're just illustrating a point...... PUN! WOO! these videos are saving my life btw. you rock!

You are amazing, thanks for making these videos... they are so helpful! I started getting A's in my exams ever since I started watching these videos. You really "saved my life" 'cause I was failing my calculus class!!!!!!!

THANK YOU SO MUCH! I have a calc quiz tomorrow and had no idea how to do this!

Absolute life saver. I'll bet you get quite a few views around this time of the semester lol.

This video is helping me out ridiculous amounts in preparation for my calculus final tomorrow! :) You're awesome, thank you for sharing your abundant knowledge of math with us in a way that is easy to understand.

@patrickJMT You are the man, Our teacher somehow explained it differently, Thank god that now i know ionization can be found by finding equa. of tangent line ! Much simpler

@cornhead1997 not: you guys... but: thanks Patrickjmt!! : )

thanks so much man! i have my ap test tomorrow and now i know how to do this! youre a life saver!

Wow. The awesome handwriting and the left hand is hypnotizing...

thank you for making sense! really like that i can understand you instead of spending time deciphering thick accents and bad handwriting haha.

well for an equation of two variables, then you would use a tangent plane approximation, and not a tangent line approximation; i would not use taylor series at all to do this

@brendabbycakes no problem : ) good luck on the final

How useful! I was having trouble with linearization but this helped me visualize more. Thanks (:

@patrickJMT don't worry, it'll be a reality one day.

@84Porsche944 ha, that is what everyone says : )

i love you. my calc teacher cant teach for crap.

one day, when i am an engineer, you will be receiving quite a donation for your countless videos that made it possible.

@jlmaricela yep, got these probs from ut

you have really helped mee soo much i aced my advance functions exam and hopefully my calc now. your videos are sooooooo helpful thanks a lot :P

One of the most common ways students are told to linearize equations is through Taylor Series (Ignoring terms higher than second order). If your function had multiple trig functions would you apply Taylor series to the whole functions, or just the trig functions within the whole function?

glad it helped!

Shoot. It's 2020 and I am watching him to help with CAL 1. I guess numbers never change.

glad the grade is better : )

Thank You! This was more insightful than the 15 minutes my math teacher dedicated to it. :D

Ok, I got this. Now lets find another of Patrick's videos.

would you apply Taylor series to the whole functions, or just the trig functions within the whole function? i dont understand what you mean here

why life gotta be so complicated. Thanks for making it simpler :D

Thank you so much for everything patrick

@patrickJMT hell yeah UT!

ha! thanks : ) we will see!

ha! nice!

you sir deserve more subscribers

I was also wondering why you wrote 12. But, thanks for the help!

thank you soooo much, my teacher said to figure it out yourself and i was freaking out :)

@bryan91292 yes, lol. i already have.

got a 5 on the AP Calculus AB test. Thanks so much!

Patrick thanks a lot, you save my life. p/s: from M'sia regards, Patrick :)

Awesome stuff! Keep up the great work :)

Thank you so much Professor lol It really really helped

Let's say f(x,y) = sin(x) + constant/cos(y). I guess what i'm asking is how you would use taylor series to linearize that equation which contains trig functions and two variables?

Just curious, is there any type math that you don't know? Your knowledge is incredible...thank you.

@ultimazer0 maybe you can go back in time 3 years and help me out

no luck needed... i need employees at this point.

Completely Agree, but its because calculus teachers think we care on how it work, but we all know that none of us care how or why it works just how to do the freakin questions get a good mark and forget everything after we pass the class, unless the nerd wants to know how or why but he already researched the shit and does it for fun :)

highschool calc ab/bc midterm tomorrow.... hip hip hooray

Hey, that actually made sense! Thanks!

damn man, you helped me a lot, thank you from all my heart

Whew. Thanks to your videos, I feel like Calculus is starting to love me back too. It's amazing how you make everything sound so easy and simple to solve than how our professor makes it out to be.

@kevtyan nooooooooooo

MORe linear apprx problemss lol :) u rockk

@guitar5499 good luck!

Thanks bro, cool video

Why did I just learn more in these 4 minutes than I did in the one hour and 15 minutes my professor spent going over this in class? SMH.

gogo patrick!

Thanks for the videos :) btw, ur using QUEST, huh? :P

Patrick...stop being such a beast at life.. or at math i should say :)

Awesome video!!

can you show us linearization of a 2nd order non linear dynamic system with two variables

This is so sick!

You should really rationalize your denominators yo! But awesome video, you are very helpful.

so it's basically the tangent line at that point?

you are a god.

still using you in college haha thanks a ton!

how do you know if it is over-estimate or under-estimate?

Shouldn't the entire radical be in the numerator EDIT: nope nvm forgot the negative

What is there are two points eg.f(x) = x^2 points (2,4)

Did you teach at UT??

: )

@xFlenchx thanks... now get off your knees.

thank you #thingsyouhaveheardbefore

why did i write 12. LOL geeking in the library

I think he forgot to multiply by 7 at 1:49

HA. Ap calc BC test tomorrow.

i

Instead of saying square root for sqrt, my family just says squirt.

Coool

dude i fuckin love you , no homo

lol. Same here.

Rip headphone users at that cough

woah

i'm lost.

fuck final exams being worth 30% of your grade. peace out

PLEASE PLEASE PLEASE come and teach instead of my teacher. Either that or I have to convince him to play your videos instead of lecturing for an hour and a half.

it must be 1/2 not -3/2

This is really only stressed in High School

LEFTIES UNITE!

You write uncommonly fast.

Too fast.

thank you #thingsyouhaveheardbefore