❖ Three Tricky Limits Involving Trig! ❖
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- Опубліковано 21 вер 2024
- Make sure you know some important limit results and some trig identities!
Here we look at limits involving sine, cosine, and tangent. A common technique to solve these types of questions is to use identities so make sure that you have a few in your toolkit.
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.
Same.. but in college. I am now a CyberSec Eng. I passed math thanks to him
Doing cal 1, wanting to become a radiologist as well!
@user-iq3uf2ls2s all the best, long journey but radiology is great!
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.
thanks :) i appreciate the support and kind words!
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
:))
that's actually incorrect logic
@@friedhegg8874 wait really? Could you please explain cause i also solved it like that.
The conjugate of 1-cosx isn't 1+cos^2 x... You freely squared cosine on denom...
i think after multiplying the conjugate with the numo then we get the eq 1-cos^2x
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!
I’m about to take a quiz on trig limits- I think this might end up saving me!
We're in friggin business baby
Where did you go? Like you haven't been around for a long time now.
burnt out on youtube. working on other projects :)
@@patrickjmt hope everything will go well for you. take care of yourself first!! you are awesome :)
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?
These questions are really very easy for a student preparing for jee advanced exam
Great video. Helped me so much...
Good stuff
JMT just like the end of Subdivisions by RUSH 👍
Thank you! You tuaght me everything I know.
I want more problems like this but I dunno where to find them
The prodigal son has returned
Simply great!!!
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.
Ladies and gentlemen, the king is back
you are too kind Mr. Newton
@@patrickjmt hats off to you
omg this is exactly what i needed
The legend returns
You are back finally 😭
this question so amazing :D thank you bro
hello, does anyone know what kind of note taking website/app he is using?
Thanks for the helpful videos, Patrick. Curious -- what app are you using to show your work?
it is called 'notability'
Dear sir ,
Can you please prepare a playlist of your math videos for jee in india.
Got your recommendation from flipping physics youtube channel.
Good job💜
What kind of device are u using to create yt lecture videos? Ipad pro 12.9 pro?
Good job
After a long time but finally.
ya, got burnt out. trying to get my second (or third or fourth or fifth....) wind
@@patrickjmt 🙌👍
Teacher how to solve lim x approach to 2
Cos pi/2 over x-2
Thanks a lot
L hopital rule laughing at the corner
will I be wrong if I just used L'Hospital's rule from the start?
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
It is really great mathematician
Long time no see SIR!
We use l'hopital also in 1st
lucky
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 ?
6:41
grind
Last one you wasted too much effort you could have just multiplied by 1+cosx on the den and nom
all questions are just an application of l'hopital rule
How are limits involving trig used by mathematicians in the real world to solve problems?
mainly limits are used in the formal definition of derivatives which have a million and one uses
@@patrickjmt Thank you?
@@marjorieromero7147 No, thank the limit for being there.
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😅😅
Is not all that clear ….your writings are not clear … if you can do something about it for us