❖ Three Tricky Limits Involving Trig! ❖

[@hussa2700]

Haven't been on this channel in a while... Taught me 11th-12th grade math back in 2011-12. I'm a doctor (radiologist) now, keep up the great work mate.

[@lyricschannel7579]

Same.. but in college. I am now a CyberSec Eng. I passed math thanks to him

[@AngelicaCapua-l9o]

Doing cal 1, wanting to become a radiologist as well!

[@hussa2700]

​@user-iq3uf2ls2s all the best, long journey but radiology is great!

[@benjamincarr9233]

Great to see you back Patrick! Your videos got me through my HND at my first university from 2016 - 18. I graduated last year with an MSc. Couldn't have done it without you.

[@patrickjmt]

thanks :) i appreciate the support and kind words!

[@BssNation]

the last limit had a much easier way to be done but thankss anyways !! by multiplying the numerator and denominator by its conjugate you get 1 - cos^2x ------------------ x^2(1 + cos^2x) then you can just convert 1 - cos^2x to sin^2x and using a limit rule sin^2x 1 ----------- . ---------- x^2 1 + cos^2x lim^2 sinx 1 ------- . ------ x-->0 x 1 + 1 (since cos(0) = 1) lim x --> 1 . 1/2 = 1/2 :))

[@friedhegg8874]

that's actually incorrect logic

[@moltenforger7295]

@@friedhegg8874 wait really? Could you please explain cause i also solved it like that.

[@triple_gem_shining]

The conjugate of 1-cosx isn't 1+cos^2 x... You freely squared cosine on denom...

[@tayfrliife]

i think after multiplying the conjugate with the numo then we get the eq 1-cos^2x

[@jacksonlanglais1404]

watching this night before the test and realised by teacher never taught us how to do this and its going to be on the test. lucky me!

[@theidiotwithinternet]

I’m about to take a quiz on trig limits- I think this might end up saving me!

[@mathsacademy3349]

Great video. Helped me so much...

[@himansu4923]

These questions are really very easy for a student preparing for jee advanced exam

[@sophiahitch726]

I want more problems like this but I dunno where to find them

[@baldaiomir]

omg this is exactly what i needed

[@saarike]

Simply great!!!

[@drumtwo4seven]

Good stuff JMT just like the end of Subdivisions by RUSH 👍

[@NolanMakatche]

Thank you! You tuaght me everything I know.

[@trevorjames4619]

The prodigal son has returned

[@RobertRaleySummers]

The legend returns

[@barryzeeberg3672]

At around 4:12, you are assuming that the lim function can be distributed among the terms of the argument. This assumption should be made more explicit, and it should be justified.

[@isaacnewton2855]

Ladies and gentlemen, the king is back

[@patrickjmt]

you are too kind Mr. Newton

[@isaacnewton2855]

@@patrickjmt hats off to you

[@Necrozene]

lim as x-> 0 of sin x over x is obvious from the Taylor expansion, yeah? Or even just look at the graph. What's so hard about proving that one?

[@shadowmoon7308]

Taylor series is not taught until way after you have these in calculus 1 or high school unless maybe ap classes but im not american so i dont know about that

[@kaizenryan3390]

You are back finally 😭

[@matiask533]

Good job

[@drbalontotis2474]

this question so amazing :D thank you bro

[@collegemath8024]

Good job💜

[@faraazshaikh3706]

Dear sir , Can you please prepare a playlist of your math videos for jee in india. Got your recommendation from flipping physics youtube channel.

[@allensnea9335]

thank you so much

[@patrickjmt]

You're welcome!

[@beto5747]

hello, does anyone know what kind of note taking website/app he is using?

[@yarawail2190]

Teacher how to solve lim x approach to 2 Cos pi/2 over x-2

[@PLP0321]

Thanks for the helpful videos, Patrick. Curious -- what app are you using to show your work?

[@patrickjmt]

it is called 'notability'

[@selcuk2649]

What kind of device are u using to create yt lecture videos? Ipad pro 12.9 pro?

[@triple_gem_shining]

We're in friggin business baby

[@patrickjmt]

lulz

[@TshegofatsoTau-b6z]

will I be wrong if I just used L'Hospital's rule from the start?

[@Philocalyleena]

Nope, actually saved a lot of time. I am currently in my second chapter of my calculus book and haven’t reached derivatives, that’s why my teacher teaches me this. He also told me once we reach derivatives, we would no longer make a use of this and use L’Hopital’s rule

[@gm0032]

After a long time but finally.

[@patrickjmt]

ya, got burnt out. trying to get my second (or third or fourth or fifth....) wind

[@gm0032]

@@patrickjmt 🙌👍

[@ebhojayejuliet9728]

Thanks a lot

[@Kazama_526]

Long time no see SIR!

[@kapeed3327]

L hopital rule laughing at the corner

[@sudhakarmathsacademy]

It is really great mathematician

[@mmd8075]

Hi, for the tan(x-2)/(x^2-4) why not use lim ->0 tan(x)/x knowing that x->2 then x-2->0 ?

[@Maths_Magic_]

We use l'hopital also in 1st

[@Ghaidaa]

lucky

[@طربوسلملو]

grind

[@Maths_Magic_]

all questions are just an application of l'hopital rule

[@salvadorsabateromero2258]

6:41

[@marjorieromero7147]

How are limits involving trig used by mathematicians in the real world to solve problems?

[@patrickjmt]

mainly limits are used in the formal definition of derivatives which have a million and one uses

[@marjorieromero7147]

@@patrickjmt Thank you?

[@glorymanheretosleep]

@@marjorieromero7147 No, thank the limit for being there.

[@amineamer6470]

Last one you wasted too much effort you could have just multiplied by 1+cosx on the den and nom

[@discoooooooo]

[@natideseye6661]

that is good but it is 2 min work for real give us a real mats. i work these with 1 min please give us real very very tricky questions and hard that you can show us if u can with in a week😅😅

[@wishborn7491]

Is not all that clear ….your writings are not clear … if you can do something about it for us

[@glorymanheretosleep]

Where did you go? Like you haven't been around for a long time now.

[@patrickjmt]

burnt out on youtube. working on other projects :)

[@ha5266]

@@patrickjmt hope everything will go well for you. take care of yourself first!! you are awesome :)