Help support the production of this course by joining Wrath of Math to access exclusive and early Calc 1 videos, plus lecture notes at the premium tier! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Calculus 1 Exercises: kzbin.info/aero/PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx Calculus 1 Course: kzbin.info/aero/PLztBpqftvzxWVDpl8oaz_Co6CW50KtGJy
@Vera-lk1vc11 ай бұрын
My native language isn't even English, but I think this explanation is better than the one that could be done in my own language.
@WrathofMath11 ай бұрын
So glad it could help!
@enochgau11157 ай бұрын
so true
@akhu123ful2 ай бұрын
same here lol
@punditgi3 жыл бұрын
Very nifty solution to the problem! The Wrath of Math always manages to squeeze the most out of each lesson! 😁
@WrathofMath3 жыл бұрын
Thanks Ezra! It's always my goal to sandwich the best math content I can between the intro and outro!
@punditgi3 жыл бұрын
@@WrathofMath 😁
@Ski49742 жыл бұрын
It's actually so helpful how you consider the other possible approaches and explain why it won't work.
@davidshi4513 жыл бұрын
I'm finally taking real analysis! You always have a knack of posting videos *just* when I need them :D
@abdallahabughazaleh92632 жыл бұрын
Thank you so much prof. the way you explained every single step and took your time with it was absolutely perfect.
@WrathofMath2 жыл бұрын
So glad to help - thanks for watching and let me know if you ever have any requests!
@applepie45853 жыл бұрын
Thank you so much for the clear explanation!! I'm struggling with calculus 1 and this was much needed.
@MarjoAla-rami Жыл бұрын
I love the way you lecture, you explain each step so clearly. Thank you!!!!! So helpful in my analysis class
@МихаилВеличковский-ы5п2 күн бұрын
Thank you very much for doing these videos!!! I think you help a lot of students all over the world by doing this!!!! I'm preparing for my test in maths right now and I'm very glad I've found your channel! Keep up the good work!! 👍👍💯
@WrathofMath2 күн бұрын
Thank you! Good luck on the test!
@melontusk73583 жыл бұрын
This vid just saved my life, dude, you've earned another subscriber. Of course, you deserve as many views and appreciators as 3blue1brown and Flammable Maths
@matthias2447 Жыл бұрын
Very well explained, especially the edge cases and your thoughts.
@WrathofMath Жыл бұрын
Thank you! Lots more in my calc 1 exercises playlist; kzbin.info/aero/PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx
@upendrakumarpanigrahi26662 жыл бұрын
The way you teach is as awasome as you.
@WrathofMath2 жыл бұрын
Thank you, glad to help!
@uzairwajeeh17372 жыл бұрын
By squeeze theorem: lim(x approaches 0) sin(x)/x is equal to one We can express xsin(1/x) as sin(1/x) / (1/x) and taking limit, it should be equal to 1 according to sandwich theorem so a bit confused as to how the evaluation of limit of this function gives zero
@WrathofMath2 жыл бұрын
Thanks for watching and good question. sinx/x is 1 as the input approaches 0, but in sin(1/x) / (1/x), x going to 0 makes the input (1/x in this case) approach infinity, so it is a different limit.
@shachisharma89082 жыл бұрын
Hey!...My name is Shachi. Thanks for Solution of each Maths problem!!!
@statusworld.c2 жыл бұрын
Hi sachi
@carolinelotte2156 Жыл бұрын
just studying for my amendatory test and this helped me a lot. going to watch other of your videos today
@WrathofMath Жыл бұрын
Good luck!
@WrathofMath3 жыл бұрын
Studying for the AP Calc exam? Go through a full AP Calc AB Exam with me in this video! kzbin.info/www/bejne/fpvCkpR8mZ6krcU
@enoq98 Жыл бұрын
what stops me from doing t = 1/x, x=1/t making me get (1/t)*sin(t) as t approaches 0 making me get the standard limit of 1
@fatimazahrazine690511 ай бұрын
such a talented teacher ;))
@WrathofMath11 ай бұрын
Thank you!
@rajpootvikram65426 күн бұрын
My teacher had thought a wrong way so I am very sad in this time because he can't understand our future days he pressed for coaching. It is totally wrong for every child. The biggest problem in our India, is coaching. So I pray to god our government must a law for coaching centre.😢😢😢
@MrAllenmath2 ай бұрын
Fantastic explanation! Kudos!
@WrathofMath2 ай бұрын
Thank you kindly!
@ronakruhal249310 ай бұрын
Nice explanation 👍👍👍👍...but can't we solve the limit such that sin(1/x) dividing and multiply by (1/x) thus it will be equal 1 and x multiply 1/x will also equal to one and the limit of any constant is 1..... So the answer should be 1 ??? If we solve in auch a manner ...
@fanfsty. Жыл бұрын
Hats off to you respect from India;)
@WrathofMath Жыл бұрын
Thanks for watching!
@faintz10 Жыл бұрын
your voice permanently altered my brain chemistry
@WrathofMath Жыл бұрын
In a good way?
@kevinabraham69083 жыл бұрын
Just found your channel today great content :) much lov ☺
@WrathofMath3 жыл бұрын
Thanks a lot, Kevin! Let me know if you ever have any questions!
@logeshvar54142 жыл бұрын
Love from India ❣️thank you for the Clear explanation
@WrathofMath2 жыл бұрын
My pleasure, thanks for watching! If you're looking for more Calculus 1 Exercises, check out my playlist! kzbin.info/aero/PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx It's an unlisted playlist right now because it doesn't have too much in it, but I am working on it!
@logeshvar54142 жыл бұрын
@@WrathofMath once again thank ..i am searching for calculus problems only..😅
@Education-353 ай бұрын
Sometime ask in between the quesⁿs of JEE advanced JEE aspirant 2025 🔥🔥🔥
@adityabaldha30828 күн бұрын
All the best👍🏻
@Education-3527 күн бұрын
@@adityabaldha308 🔜🔜🔜
@orang1921 Жыл бұрын
man, that's crazy. love calculus.
@WrathofMath Жыл бұрын
Me too!
@aanchalsirohi897111 ай бұрын
Thanks from India 🎉😊
@WrathofMath11 ай бұрын
Most welcome 😊
@anshikaarshi83792 жыл бұрын
Thanks a lot. I have a question that can't we write the x which is beside sin(1/x) as : {sin(1/x)}/(1/x)=1 And this way solve? 😅
@johnsu99492 жыл бұрын
nope, you can't use the property lim x-->0 sinx/x =1 here because the angles inside approach infinity and not 0.
@drofeng Жыл бұрын
you can write lim(x->0) sin(1/x)/(1/x) Let u = 1/x As x->0, u->infinity, so we get lim(u->infinity) sin(u)/u sin(u) keeps oscillating while u keeps getting larger, so the limit evaluates to zero
@Izmoa Жыл бұрын
Thanks for the help
@mergup17 Жыл бұрын
Thank you so much
@jiajia18162 жыл бұрын
thanks for good concept
@vaishnavi2612 Жыл бұрын
Nice explanation🎉❤
@225hauzel92 жыл бұрын
U clear my problem,new subscriber 🌚, keep it up 💪
@WrathofMath2 жыл бұрын
Thanks, glad it helped!
@3467AAA2 жыл бұрын
Loved it. Thank you :)
@WrathofMath2 жыл бұрын
My pleasure, thanks for watching Edgar!
@zeynepthemartian6423 Жыл бұрын
how to prove this definition with using formal definition of a limit ? ( it was quite helpful video by the way, subscribed very quick!! thank you)
@isharauditha42573 жыл бұрын
super cool explanation I love it
@WrathofMath3 жыл бұрын
Thanks a lot for watching!
@chanuna2 жыл бұрын
thank you so muvh for your help!!
@WrathofMath2 жыл бұрын
My pleasure!
@glaratalib411 ай бұрын
lim_(x→0) (cosx) ( sin ( 1/x )) What’s the answer ? I mean limit does not exist
@nassouroudinenjoya79192 жыл бұрын
Merci beaucoup
@safaa142 жыл бұрын
talented 🤗
@WrathofMath2 жыл бұрын
Thanks for watching!
@zeus_rovn2 жыл бұрын
Thank you so much, and now i understand this exercise
@WrathofMath2 жыл бұрын
Glad to hear it, thanks for watching!
@doolydoko85372 жыл бұрын
From morocco ty so much
@WrathofMath2 жыл бұрын
My pleasure, thanks for watching! Check out my playlist for more calc 1 exercises and let me know if you have any requests! kzbin.info/aero/PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx
@hhoopplaa Жыл бұрын
this was very helpful. one minor question about the method though: if I used squeeze theorem on the absolute value of a function f at a point say c, and by squeeze theorem I found g(x)c) h(x) = L then can I say lim(x->c) f(x) =+-L , i.e. plus or minus L?
@WrathofMath Жыл бұрын
Thanks for watching and good question! No, because it could be that f(x) approaches L from the left, say, but -L from the right.
@hhoopplaa Жыл бұрын
@@WrathofMath Ah makes sense I think. Thanks a tom for the quick answer, didn't expect that^^
@zeeshannaeem8432 Жыл бұрын
Tnk you sir.
@WrathofMath Жыл бұрын
Glad to help!
@takumifujiwara2073 Жыл бұрын
THANK YOUUU
@WrathofMath Жыл бұрын
Glad to help!
@odichamathew17003 жыл бұрын
Very useful thanx😇🤗
@WrathofMath3 жыл бұрын
My pleasure, glad it helped and thanks for watching! Here is a link to my Calculus I playlist if you're looking for more: kzbin.info/aero/PLztBpqftvzxWVDpl8oaz_Co6CW50KtGJy It's currently unlisted because I haven't put many videos in it, but I am continuing to work on it, let me know if you ever have any questions!
@ayansuleymanova032 жыл бұрын
thank you!!! keep going :)
@WrathofMath2 жыл бұрын
You're very welcome, I will! Let me know if you ever have any video requests!
@radhas_reverie6 ай бұрын
Thanksss❤
@sasindudilshan66792 жыл бұрын
Very good explanation sir💪
@WrathofMath2 жыл бұрын
Thank you! I've got plenty more Calculus 1 exercises in my playlist, and am happy to make more if you have any requests!
@sasindudilshan66792 жыл бұрын
@@WrathofMath please make videos sir ❤❤ they are really helpful 😊😊
@mohammadhasibemran5955 Жыл бұрын
did youtube forget to compress ur videos. why is it so HD lol. also ebic video. liekd and subskrieb'd
@WrathofMath Жыл бұрын
Thank you! I record in 4K with a very nice camera - I take pride in going overboard for quality for simple math lessons. "simple" in some ways and not others I suppose.
@kwpogromca2 жыл бұрын
I'm wondering if is it scientificly correct to do it a bit diffrent way. I mean of course you cant just substitute x's with 0 because that would lead to 1/0 but if you do it like that: sin is always [-1,1] that implicates the solution is 0 times value from range [-1,1] and that is always 0 So a bit more theoretical approach instead of just stright up calculating.
@WrathofMath2 жыл бұрын
Thanks for watching and the question. I'd say that isn't a different way, it's just a less rigorous description of the way we did it. The sine function is between -1 and 1, and the factor of x will make it approach 0. There are different ways we could take care of the squeeze, but the ideas are all pretty similar.
@joannaaabui9 ай бұрын
NICE VIDEO
@thejahafamily2 жыл бұрын
Love from Pakistan ❤️🇵🇰
@WrathofMath2 жыл бұрын
Much love back from the USA's east coast! Thanks a lot for watching and let me know if you have any questions!
@thejahafamily2 жыл бұрын
@@WrathofMath Sure ❤️ with Lots of Love ☺️
@VioletMemories2 жыл бұрын
wait, why are we using absolute values? Why is -1
@WrathofMath2 жыл бұрын
Thanks for watching and for the question, Miranda! You could have just split this up into a left and right hand limit, show they're both 0, and so the limit is 0 if you preferred. The benefit of the absolute value is that it allows us to avoid splitting the limit into two parts, because whether x is approaching from the left or the right, the absolute value of everything stays the same. So we end up with a proof about the limit of the absolute value of our function. Normally, the absolute value of a function having a particular limit tells you nothing about the limit of the original function EXCEPT in the case where the limit is 0. In this case, we found a limit of 0, which does apply to the original function as well. Again, if the limit of |f(x)| at some point is 0, then the limit of f(x) at that point is 0 as well. I'll do a video on this result eventually, but this is a video I did proving the result for sequences, which may be overly complicated if you're just studying Calc I: kzbin.info/www/bejne/d6PMdp5phqlksJI Does that help?
@VioletMemories2 жыл бұрын
@@WrathofMath a bit, but why do we cut out the negatives? Is it because of symmetry and we only need to focus on one side?
@Browlet540Ай бұрын
Symmetry, @@VioletMemories
@ParaPsychic3 жыл бұрын
Can you do Cayley's Theorem? There are n^n-2 labelled trees with n vertices, n>=2
@monky25142 жыл бұрын
could you not have multiplied x to -1
@WrathofMath2 жыл бұрын
Thanks for watching and good question! The problem with that is that x is approaching 0 from both sides. So, when you multiply everything by x, you are multiplying by something that can be negative. When x is negative, xsin(1/x) is less than or equal to -x. Absolute value helps us smooth over that mess!
@malakfalkoun12802 жыл бұрын
can we use the same method with tan ?
@taiduan25010 ай бұрын
Does this method counted as analyticall?
@mazlumdemir227 Жыл бұрын
sorry ı did not get one part of that. What if you multiply the function with (1/x)/(1/x). And ıf you go on you will get x*(1/x) * sin(1/x)/(1/x) and ı got the answer 1
@MathCuriousity Жыл бұрын
oscillates between what and what?
@marian_ebenbichler Жыл бұрын
is this method also possible with the cosinus?
@WrathofMath Жыл бұрын
Yup! Nothing special about sine in this example!
@tanaka39532 жыл бұрын
The answer is actually 1
@raiza_sabila Жыл бұрын
How if lim x->0 x sin (1/x²) sir? Thank you for your videos its very help✨
@WrathofMath Жыл бұрын
Same strategy will work!
@raiza_sabila Жыл бұрын
@@WrathofMath thank you sir🙏
@raiza_sabila Жыл бұрын
@@WrathofMath the answer is same sir?
@diwakar500 Жыл бұрын
@@raiza_sabila yes the answer is zero for any positive power of x multiplied by sin(1/x^k)
@raiza_sabila Жыл бұрын
@@diwakar500 thank you sir🙏
@buiquangtuan18342 жыл бұрын
thank you so much 0
@ahmedelkhomsy27113 жыл бұрын
Very good 👍👍
@WrathofMath3 жыл бұрын
Thank you!
@ahmedelkhomsy27113 жыл бұрын
@@WrathofMath i have a question lim [x]sin(1/x) x->0 = 0 ??
@WrathofMath3 жыл бұрын
I'm not sure what you mean, that's precisely the limit we evaluate in this video!
@stkhan19453 жыл бұрын
@7:28.. .it's getting arbitrarily close to zero ....should it not be ..its getting incrementally closer and closer to zero ? ..instead ..
@SangTran-ch8wo Жыл бұрын
how about limit of xtan(1/x) as x goes to 0
@WrathofMath Жыл бұрын
That one doesn't exist since tan(1/x) = sin(1/x) / cos(1/x). So as x goes to 0, the 1/x terms will approach infinity and will cause rapid oscillation near 0 as well as being undefined at all reciprocals of odd multiples of pi/1, since those values will make cos(1/x) = 0.
@kumarrajiblovely44902 жыл бұрын
Very nice solutions but I am not catch
@WrathofMath2 жыл бұрын
Thanks for watching! I'm not sure what you mean, did you have a question I could answer?
@akkamal6999 Жыл бұрын
what's the outro music?
@Nidhisahu12310 ай бұрын
I am watching this video in India ❤
@WrathofMath10 ай бұрын
Thanks for watching!
@nishantmudgal44342 жыл бұрын
Why sin (1/x) didn't approached to ∞ at Lim x ----> 0 😑😑
@WrathofMath2 жыл бұрын
Thanks for watching and for the question! Why would sin(1/x) approach infinity? Remember the sine function is always between -1 and 1, so there is no way it can approach infinity. The input, 1/x, is going to infinity as x goes to 0, but that doesn't make any difference as far as sine is concerned, it just oscillates between -1 and 1 as always. Hope that helps!
@nishantmudgal44342 жыл бұрын
@@WrathofMath I'm sorry Bruh actually I'm dumb at maths, and was stuck in this doubt yesterday, but i realised what I'm asking doesn't make sence, as i thought The Whole function became ∞, I Didn't Payed attention that only the angle has become ∞, and sine function still lies between -1 and 1. Sorry 😅😅
@englishbaba65662 жыл бұрын
My master said it a wrong method??
@WrathofMath2 жыл бұрын
How do they expect you to do it? There are multiple ways, but this way is certainly fine.
@Zozo-xh7jj3 жыл бұрын
Can you please do the proof of lim sin1/x x--->0 Is failed to exist
@WrathofMath3 жыл бұрын
Thanks for watching! I could do a video explaining why that limit doesn't exist, which would fit nicely in the Calculus playlist. If you want an actual proof, I could do that too in my Real Analysis playlist - that would use a theorem regarding the limits of functions. Something like...look at this sequence a_n that converges to 0, and this other sequence b_n that converges to 0, but notice f(a_n) converges to L1 whereas f(b_n) converges to L2, and thus f(x) has no limit as x approaches 0. So are you looking for an explanation or a proof like I described?
@Zozo-xh7jj3 жыл бұрын
@@WrathofMath it was so clear thanks i’m looking for a proof using the definition of limit something like If |x_a| |f(x) -l|
@reno39552 жыл бұрын
Heyyy there Thank you so much for the video I love how you explain all the details ♥️♥️♥️ + Can you please help me with this proof: Lim (x/(2-sin²x)) x->0 I need to write an epsilon delta proof .. I’d really appreciate your help ♥️
@WrathofMath2 жыл бұрын
Thanks for watching! That should be pretty straightforward if you work with it a bit. Have delta equal to epsilon, then you'd have |x - 0| < delta < epsilon. But 2-sin^2(x) >=1 and so |x-0| = |x| < epsilon
@redred5195 Жыл бұрын
guau thanks
@neetutripathi9438 ай бұрын
Where do you live???
@shriyasachdeva10247 ай бұрын
the minecraft lucky block-
@WrathofMath7 ай бұрын
Is that what kids call the Mario question block these days?
@shriyasachdeva10247 ай бұрын
@@WrathofMath maybe
@shriyasachdeva10247 ай бұрын
@@WrathofMath anyways thanks for the explanation sir