Limits of Trigonometric Functions

[@TheOrganicChemistryTutor]

Limits - Free Formula Sheet: bit.ly/3T3dD2X Final Exams and Video Playlists: www.video-tutor.net/ Calculus 1 Final Exam Review: kzbin.info/www/bejne/jZ6lq6B-p9pqbtk Next Video: kzbin.info/www/bejne/rqepoqKjhNV_qNU

[@MikeChipili]

😮

[@mattdan265]

Are you able to prove that (3w/sin3w)=1, because the only thing I could remember in my calculus class is to prove that (sinx/x)=1. Or do you take a resprocal of it?

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when you said "make sure your calculator is in radian mode by the way", the world made sense once again.

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[@wm396]

How do you do that

[@mya4855]

@@wm396 depends what calculator you have?

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ur comment is a life saver

[@wenwen8237]

can anyone answer me why it should be radian mode btw

[@jemilieredito2498]

(sin x) (x) = x sin x (sin x) (sin x) = sin^2 x So it should be limit of sinx/x as x approaches 0 times limit of sin x as x approaches 0. Though the answer is still 0, there’s a problem in the process. Thanks.

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Thought i was the only one. (^^)

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I was literally looking for this comment

[@Bromosomo]

preach

[@DEYIINTEL]

I thought I'd be the first to correct this but here it is

[@FlowinZen]

This correction is for what time in the video?

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Listen my math prof has been trying to teach this for weeks and when you hit that opening statement and explained it in a way that made sense i nearly came

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oh my god, thank you so much for mentioning that the calcu should be in radian mode. I've been crying over my wrong answers for weeks, this is my 3rd breakdown this week and I can finally answer my long overdue assignment, thank u so much, may you be blessed for the rest of your life and the next.

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He's a gem. My real teacher in all my math sequence. I tip my hat for professor Leonard.

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[@tysonkoch468]

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[@lazsa3433]

Good job brother, you made a mistake in question 14:00 minutes but the answer turned out the same. Your saving my life out here

[@stefexx7691]

This man blessed me before my limits exams

[@husseinalhadi5471]

Excellent video at 13:43 mark shouldn't Sin ^2 = sin (x) X Sin (x) not sin (x) X x

[@agent-if9jb]

agreed.

[@marknzuri9119]

Yeah I thought so too!

[@aliu760]

yeah I saw that mistake

[@benjaminm3180]

Since sin(x) using the unit circle equates to zero, and x is approaching zero (so you plug in zero), either way you write it will be multiplying by zero. I’ll admit I had to pause the video to think about it for a minute to completely understand what he meant but the way he wrote it is still technically viable.

[@silas_mwanikitv]

Yeah! Sure

[@xenovos8895]

Thanks!

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[@nerijoyceobedoza26]

We don't even allowed to use a calculator😭. They required us to solve it manually

[@abivander]

me too, havent been able to find a video that explains how to do this without using a calculator. so stupid i give up and my exam is tomorrow

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[@ianruiz6350]

I'm just here scrolling down through comments seeing everybody somehow understanding even though he never explained the why of things. 3:14 how did he know that he had to multiply by 5? 5:39 how did he know he had to multiply top and bottom by 2? 7:33 how did he know he had to do THAT? I just don't see a pattern at all. It feels like he's explaining how to do the specific problems rather than teaching us how to analyze problems on our own. I'm gonna be solving all of these thinking I understand them then when the tests arrives I won't even be able to know where to start or how to tackle the problem.

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up

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[@nickpetrowski7182]

Can we all agree that him showing the answers before we show our work is a huge help? For me it helps concrete in how i got to the answer.

[@enviableace9987]

6:06 Took me a while to understand why you switched the places of the 2 and the 5, the only reason is because when you work out the expression, it would equal the same thing if you didn't switch them, I have never seen this strategy before. GENIUS!

[@AstersSpam]

You are singlehandedly carrying me through my AP Calculus course ILY

[@glitxh6147]

this is actually such a straightforward and simple explanation thank you very much for making this video it saved me in AP calc since I was trash at trigonometry.

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Im just a bored yr9 kid, I now know how to do basic Limits thanks to this guy! 👍

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[@pllimboy]

this video was very helpful for my online classes in calculous. Its hard to learn math through just pdfs. Glad I saw this!

[@laizat.1300]

Isn't it that sin^2 x = (sin x)(sin x)? Why is it that at around 13:36 of this video, the sin^2 x became (sin x)(x)? Although, the final answer is still gonna be the same. I just got confused. I am hoping for your reply. Thank you. :)

[@m.rizaarrafi411]

i was about to say that, i think he made a little mistake right there

[@guycha0s380]

Yup, it's a mistake

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i thought i was retarted

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Yes

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Looking at the comments checking if I'm the only one. 😆

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you helped me in 1 question but you already deserve a thanks. Thanks!

[@ninjanigabiyown4253]

The problem where there is sin²x It should be (sinx)(sinx) instead of (sinx)(x).

[@evansraila5519]

It'll still be the same i think...

[@Bbqeee]

​@@evansraila5519 yes bc (sinx/x) will be 1 And as x→0 (sinx) will be 0 So 1*0 will be 0

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[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for calculating Limits of Trigonometric/Transcendental Functions in Calculus. Thanks to the viewer(s) for correcting the error on (Sinx)^2/x in the video. Although the final answer is correct, the method is incorrect.

[@ashleyfontanilla2262]

There is a better way to approach the problem presented at 6:00, in case if anyone is confused by the arbitrary, "just switch the 5 and the 2." Instead of "just switching," multiply the numerator and the denominator by 2/5 to maintian a logical approach. In the denominator the 5's cancel out leaving a 2x, and just keep the 2/5 that pertains to the numerator on the outside as it was exemplified in the previous problem.

[@scarleteyes415]

Very easy way to do it: Before multiplying anything, we have the fraction "sin(2x)/5x". Since the fraction is already divided by 5, we take 1/5 outside the limit, so the fraction becomes: 1/5 (lim sin2x/x). Now we just solve it like we did in the previous question, the only difference is that we have 1/5 outside the limit. We multiplay the equation by 2/2 and we get: 1/5 (lim 2sin2x/2x). Now we just take out the 2 in the numerator outside the limit the same as the previous question, hence it's multiplied by 1/5 that is also outside the limit: 2/5 (lim sin2x/2x). So, we put Y = 2x and we get: 2/5 (lim siny/y) as y goes to zero, so the latter term is equal to 1, therefore 2/5 (1) = 2/5

[@heavysaber9431]

I agree, his methods are somewhat unorthodox to a logical approach to math, but it still works anyhow. Still, its better to have general logic in tackling these problems instead of just "switch these numbers" without knowing the reason why or how the value within the function should still remain the same while arranging the numbers, manipulating numbers isn't that simple.

[@miguelconfesor4701]

The 2 and 5 can be switched because we are dealing with multiplication.

[@bsflipgawd8238]

Thank you for existing. Your videos saved my ass from failing multiple classes. God bless sir.

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I have my geg exams coming up and I just started studying a week before, this video has been very helpful. I had zero idea before this video, you’re amazing keep up the good work!

[@mackenziekolb5936]

I finally understand how to do this after struggling with it for 3 years... thanks dude

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I loved the vedio soooo much it was so freaking helpful please please do more vedio on more complicated problems. Plleeaaassseee!!!!!

[@user-xq3jq3cf2f]

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The only channel with 0 negative comentss 😂

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[@X1GenKaneShiroX]

Trying to find the limits of trigonometric functions are probably one of the most complicated things when entering to the realm of calculus.

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God speed. I wish you good life and health to be able to make more educational videos like this because it helps a lot. Thank you

[@kamrulhaquealmi2693]

if you're looking for why to use radian? then here's an explanation - In radian we use number, like the pie itself, π=3.1416... in degree which is equivalent to π radians=180° So, if you look into the function like sinx/x, in here x=some number; because lim(x→0) not x→0°. x does not mean degree of any angle...that's why we have to use radian.

[@tulmajok3562]

I preparing for my semester exams 📝 this help 🆘 thank you so much...

[@signingoffbye]

guys u don’t need radian mode for it and easier way would be just writing pie as 180 and you’ll get it all. for example pie/2 is 90 degrees, u can simply just do 180/2 and you’ll get 90 or another example 2pie it’ll be 180 x 2 which would be 360 degrees or a harder example 3pie/2 u would simply do 3 x 180 which would be 540 then divide it by 2 and you’ll get 270. thank me later!

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thank you king u carried me in physics last year and ap calc this year

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The first opening sentence. Thank my dude everything make sense now.

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how come this man can teach me more in 15 minutes than an 80 minute calc class?😂

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Thank you so much I owe you my life

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this genuinely saved me thank you so much

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ur videos are very helpful thaaaaaank youu and god bless you

[@reenweru9416]

I had given up on this until you said "make sure the calculator is on radian mode"

[@ems789]

Hi, not sure if youre still answering questions on this vid, but at 13:35, you said how sin^2(x) was the same as (sin(x))^2 but when written out, you put Sin(x) times X instead of Sin(x) times Sin(x). Am I thinking of it wrong?

[@JKMath]

That was a mistake on his part. You are correct! It should have been sin(x) times sin(x), not sin(x) times x.

[@ems789]

@@JKMath Omg thank you! I thought I was going insane lol!

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you made this so easy to understand thank u bro

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Great thanks to the voice behind the video

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I love you thank you you saved my life

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Thanks bro! I survived in my test because of this video!♥️

[@mattmo8648]

at around 6:50, you change around the lim to y instead of x, creating y=2x. why not just stay with sin2x/2x, and make it equal to 1? what is the reason for switching over to the y based equation?

[@mattmo8648]

side question - where do you pull the 4/4 from at 11:27? i understand the tan 4x, but are we not multiplying by 3/3 because 3x got moved? what about x/x? the last problem made me think we had to use each independent variable. i'm a little confused on that.

[@JKMath]

The reason he switches to y is to show you that it is still a form of the same special limit. That step is not completely necessary in your work, but he does it anyway to remind you that it is a special limit that is equal to 1. So in the end, all you need to know is if you have the limit as x approaches zero of sin(x)/x where as long as whatever is inside sin is also in the denominator, the limit is equal to 1. Hope that clears things up for you!

[@JKMath]

@@mattmo8648 For your side question, what you need to know is that you are always allowed to multiply by a form of 1. Anything divided by itself is 1, and multiplying anything by 1 does not change that value. So, since 4/4 is just equal to 1, we can multiply it by the limit and that allows for the use of the special trig limit. We are not multiply by 3/3, instead the 3x in the denominator was just moved out so that it is easier to see where the special limit is located. So, when determining what form of one to multiply by, look inside of your trig function (in this case sin(4x) ), and whatever is inside, you want that to be in the denominator. That's why you multiply by 4/4, because then there will be a 4 in the denominator that is multiplied by x that can then be moved under sin(4x) to then create a form of the special limit. I hope this makes sense, if not (this can be difficult to describe with just words), feel free to check out my own tutorial video on this topic that is on my channel, I'll link it here for you. I have all kinds of calculus tutorials that you may find helpful! Here's the link: kzbin.info/www/bejne/gaDHnql6rqyNpqs

[@nonhlakaniphomkhulisi1210]

Thank you so much....You're such a great teacher by the way😊🙏🙏

[@pratikshatumbapo5171]

this man's a genius.

[@HypedRogue]

Loved this video it really helped me catch up in my calc classes- one problem near the end though, I'm pretty sure sin^2(x)/x does not equal sinx/x*x, it equals sinx/x*sinx, although the limit still comes out the same.

[@gaiga494]

x*sinx/x you mean, but yeah limit comes out the same since sin(0)=0 and 0=0

[@sugarbibi5359]

dude, your explanation is easier to understand than my teacher's

[@killer0200318]

I found the sin7x/sin3x strategy very helpful.

[@charliebardey1990]

can someone explain why at 13:48 (sin^2 x)/x becomes (sinx)/x * x???

[@scienceappreciator]

typo

[@charliechaplin53]

i think there was a mistake instead of sinx*sinx, you wrote sinx*x. Infact limit when x approaches 0 of sin^2(x)/x = 0

[@Ale-lb8zm]

Thx for ur video soooo much cuz we really get a terrible textbook for calculus QAQ

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You went crazy in this vid 🤞🤞🤞

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Thank you.

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Dare I say you make calculus... FUN !

[@NatashaChigumira]

14:03 isn’t sinx • sinx not sinx •x

[@TheHamoody100]

You are right, I believe he made a mistake. And if we follow along with that, sin(0) would equal 0 too(but keep in mind that cos(0) equals 1 so don't confuse them if another problem asks). So the final solution is still the same.

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I came here because my professor needed me to evaluate limits of trig functions involving ln but without a calculator on an exam

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You're a hero..😭