How to Find the Limit at Infinity (NancyPi)
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- เผยแพร่เมื่อ 2 ต.ค. 2024
- MIT grad shows how to find the limit as x approaches infinity or negative infinity. To skip ahead: 1) For a POLYNOMIAL or CONSTANT in the limit expression, skip to 1:56. 2) For a RATIONAL ("FRACTION") expression in the limit, skip to 8:49. 3) For something of the form (SINX)/X, skip to 23:01. and 4) For an EXPONENTIAL example, skip to 27:27. Nancy formerly of MathBFF explains the steps.
For LIMITS at a FINITE VALUE (not at infinity), jump to the video: • How to Find Any Limit ...
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1) For a POLYNOMIAL or CONSTANT in the limit expression: the limit of a CONSTANT (just a finite number like 3), as x approaches infinity or negative infinity, will just be equal to that same constant number. For the limit of a POLYNOMIAL (such as 2x^2 + 2x + 5), as x approaches infinity or negative infinity, just focus on the leading term (highest x power term) in the polynomial, usually the first term. You can ignore all lower terms, because as x gets infinitely large (in either the positive or negative direction), the highest term is growing most quickly, and the lower terms will not affect the limit value. Then figure out whether this leading term will grow toward positive infinity or negative infinity, as x gets extremely large. For instance, if the leading term is 2x^2, as x goes to positive infinity, this leading term will also go toward positive infinity, and the limit will be positive infinity. If the leading term were -2x^2, the x^2 would go toward infinity, as x goes to infinity, but because of the -2, the limit is negative infinity. For X approaching NEGATIVE INFINITY, keep in mind that a negative number, to an even power, becomes positive. A negative number, to an odd power, stays negative. For instance, what if the leading term is 4x^3, and you want to find the limit as x goes to negative infinity? If you think of plugging in a very large negative number for x, the 4x^3 would still be large and negative because of the odd power. The term would go toward negative infinity, so you can write that the limit is equal to negative infinity.
2) For a RATIONAL ("FRACTION") expression in the limit: I show a shortcut (and also the official formal algebraic method) to find the limit, as x goes to infinity or negative infinity. For the SHORTCUT, there are three cases: 1) If the DEGREE OF THE NUMERATOR IS LESS THAN the degree of the denominator, then the limit is equal to zero, no matter if x is approaching positive infinity or negative infinity. 2) If the DEGREE OF THE NUMERATOR IS EQUAL TO the degree of the denominator, then the limit will be equal to the ratio of the coefficients of the leading terms of the numerator an denominator, no matter if x is approaching positive infinity or negative infinity. For instance, if you're finding the limit of the rational expression (2x^2 - 5x)/(8x^2 + 3x), as x tends toward infinity or negative infinity, the limit will be equal to the ratio 2/8, which simplifies to 1/4. The limit equals 1/4. 3) If the DEGREE OF THE NUMERATOR IS GREATER THAN the degree of the denominator, then the limit will be either infinity or negative infinity. For ex., to find the limit, as x approaches infinity, of (3x^2 - 2x)/(x + 5), instead focus on finding the limit of the ratio of leading terms, as x approaches infinity. So instead, you can find the limit of 3x^2/x, which simplifies to the limit of 3x, as x approaches infinity. Since 3x goes toward infinity, as x goes to infinity, the limit is infinity. NOTE: if x had instead been approaching negative infinity, the limit of the original expression would have been negative infinity, since 3x goes to neg. infinity as x tends to neg. infinity.
3) For something of the form (SIN X)/X: there is a trig property you can use to simplify: that the limit, as x approaches infinity or neg. infinity, of (sin x)/x is equal to 0. If your expression isn't exactly (sin x)/x but instead has something like 2x or 3x inside the sine function, like sin(3x) over x, you can use the same property but first have to rearrange the expression in a way that matches what you need. Be careful not to confuse this property with another, very similar, (sin x)/x expression for when x is approaching 0. That property states that the limit of (sin x)/x, as x approaches 0, is equal to 1. Check out my video on how to find the limit, at a finite value, for how to use that property.
4) For an EXPONENTIAL in your limit expression (with a negative power): for instance, if you are finding the limit, as x approaches infinity, of e^(-2x), first rewrite the expression using the reciprocal instead of the negative power, so 1/e^(2x). Then it is easier to see what happens as x gets extremely large and goes toward infinity. The e^(2x) gets extremely large, so 1 over a very large number will head toward zero, and the limit will be equal to 0.
For more of my math videos, check out: nancypi.com
Why don't teachers teach like her? My professors teach something simple like "1+1" then give us homework like"If Timmy left home at 9pm, how much does the moon weigh 2.5 million years ago in the future?"
Jus dumb shhh
Its cause the vast majority of math teachers have ZERO business teaching anything at all.
Fr fr
I almost peed myself reading your comment....damn that was funny.
So harshly true 😭😭
Do you guys feel that she explains better than DR and teachers in University
if she taught I'd take calc online from whatever school she was teaching
Yes 👍
literally revising for exams rn
So much easier to understand
Hell yeah
Nancy I dunno how to put into words how much I appreciate your videos. I just started taking Calculus 1, I'm learning about limits and continuity/discontinuity right now and your videos are helping so much.
Where are you at now after 2 years?👀
@@sebastianp994 3 years
@@sebastianp994 where r u after one year😃
have u d1ed?
@@ahmedwagdy8432 where are u after 4 months
Today is my first day studying calculus. I just finished reviewing your limit videos I'm feeling pretty confident about limits. Thank you for the excellent explanations on how to solve limits! :)
I'm in grade 12 right now and ever since finding this channel, I'm FINALLY able to breath and study knowing that I understand what the teacher is talking about. I've watched all the videos on the channel (this is my 3rd time watching this vid) and I'm finally confident that I can do this. I have a test on limits tomorrow so wish me luck!!!!!
me to
How did you do?
Best of luck
its been one year how did you do?
@@xXTheDemonK1ngXx i did amazing, I got an A and I got in u of t
oh my god your videos are so helpful, probably one of the best, if not the best youtube instructors i've found for calc/precalc in my many hours of searching the web. so clear and simple, explained in simple terms, good examples, well lit and neat handwriting, organized well, clear speaking, the whole package. thank you so much.
Hello, Nancy! I'm in grade 12 and taking Calculus I, and I'm so thankful for your videos. You make it so much simpler to understand. Thank you so much, Nancy!
PLEASE do continuity
Do some more limits.
QUEEN OF MATH
+
@@SydtheKyd -
Yes
For me she is my Queen of Heart...
@@edgarvicente8859 siiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiimmmmmmmmmmmmmmmmmmmmmmppppppppppppppppppppppppppppppppppppppppppppppppp
This is making Maths very intersting.
When ever it comes to searching a Math help I remember this channel.
Thanks for the amazing explanation Nancy
Keep going, I am in love with your videos. You make it seem so simple and explain it in the most basic way for everyone to understand. Thank you so much.
You explain limit better than anyone else! You've made this so simple to understand for me thank you for making these videos!!
Thank you so much for helping me in math but I would appreciate it more if you drop your skin routine 💕💕
srsly you need more subscribers. you've been helping me so much through college!
Nancy, if you are reading this please just know I am so grateful for your videos... so many difficult concepts explained perfectly... Thank you so much!!!
I was trying to recall the topic to help my son whose school is closed due corona pandemic and I went through all her limit vedios in one go . Brilliant .
Nancy>>>Keep helping us.God will bless you
Thanks from my side.
thank you, you are a life saver, i dumped math since i took calculus when i was in my bachelor courses, now i am a full time employee for a firm, the only reason why i still use advanced math is because i am doing programming and development
Nancy. Euler's great granddaughter. 😀
Yeah, to Euler little Nancy was always his number e.
Tf
@@leovolont 😂
You did a better job of explaining this in 30 minutes than my professor did in 80 and my textbook did in 20 pages. This truly highlights how vital proper teaching methods are for the students' comprehension of the material. Thank you!
Came here to get help for my calculus test today. Instead I just fell in love
Yeah, it's good to take a Cold Shower first so you can pay attention to what she is saying.
AND she could do your math homework for you!
ChiCharrone Jr Cringe
I learned calculus and fell in love!!
I got the same feeling every time I watch some of her math tutorial videos.
I am feeling like crying!!! Why I find her today not before!!! OMG!!! Thank You Sooooo Much Dear
She explained how to find derivatives exactly as my Calculus teacher explained today
I wonder if he saw your video before class.
Wow, you are so lucky to have a teacher explain like this
My teacher all the time just writes on the blackboard and then wipes
And am studying that shit at grade 12th.
Same with me, I am studying this in 6th grade
Well guess what im not gonna need to study this shit anymore. Exams cancelled. Promotion granted😀😀😀
🤍i completed mechanical engineering (diesel) from college and industrial engineering higher certificate at university for maths, your videos helped me a lot nancy 🤍 much appreciating💥❤
I just started calculus and was lost beyond belief. This is the only thing that has made any sense for me :D thank you
WE LOVE A LEGEND
I literally love you so much you're changing my whole calculus experience! ugh sooooo grateful for you!! THANK YOU!!!
I’m amazed at how she’s able to write in reverse.
I think she just mirrors the video lol
bruh you really think she writes it in reverse lol
@@elisiajimenez5527 could you explain how to do it
@@mustafarasul1346 r/woosh
Nancy thank you so much! You explained this better than any teacher I know.
I usually never comment on youtube videos but I just had to say how much this has helped me. THANK YOU SO MUCH and never stop making math videos!! :)
THANK YOU SO MUCH! My calc prof sucks and these videos have helped me so so much
Thanks for this video! In 30 Minutes I understood what 6 Hours of Classes couldn't achieve..
thank you so much, Nancy. You are doing an amazing job
I wish these kinds of videos existed back when I was in college (1980, give or take.) I would have done much better.
Yeah, but back then it was a War about the Best Textbooks. but, yeah, Information was different in those days. To KNOW anything back then, you had to subscribe to some Specialty Magazine (Mathematics Magazine) or join a club. But, yeah, you just couldn't Google anything back then. You knew or or you didn't... researching anything was like climbing Mount Everest without a sherpa.
What comes to mind is the infinity between the eye gates and the ear gates. Terrill TC!
thanks to your help, i can slide through my hw. saving myself hours of agony.
I think just me and you who are new to see this video lol
I would have never know that infinity had a limit without you Nancy...
plot twist: she doesn't fast forward her drawing/writing, she is actually a robot or superhuman and just does it at super speed
The way you explain the expression it's soo adorable ❤️
My GOD I can't focus I always get destructed by her smile
Like bro ..lmaoo
I can’t even focus, she makes sense but she keeps trowing off my concentration every time she smiles. ♾ smile 😊
Why do I get the vibe of Dakota Johnson from Nancy because of how she talks in a calm and chill manner. Lol
You're great at explaning but can you also explain what you do to your skin? Because it's glowing so much
not gonna lie, its hard learning when the teacher's hot 🔥
Thank you for this video. Gave me a nice overview because the explanations are so clear and easy to follow. Appreciate it!
I love you Nancy! You are helping me through engineering one class at a time.
She’s such an expert 👍🏻I learned within afew minutes ❤️
This was very well explained! Who else comes to her videos straightaway when you don't understand a topic in the class? *.*
Hi Aymoreno, you asked six months ago " Who else comes to her videos straightaway when you don't understand a topic in the class? " Well, I watch Nancy Pi's Calculus Videos BEFORE going to class so that I will already know WTF is going on and so my eyes won't glaze over.
I would come to her videos even IF I understood the topic in class
I like the way you explain.. So relaxed.. Beautiful and talented teacher ... Amazing way to teach.. Beautiful smile..
She's so ridiculously pretty..
Thank you so much, Nancy! I am so happy I found your channel. So helpful.
Functions or expressions may have a limit at infinity but Nancy has no limit in mathematics :)
The most beautiful MATH teacher I've ever seen.😍
So for rational expressions limits to infinity are the horizontal asymptotes?! 🤯🤯🤯
Hi MrREmm, You say "So for rational expressions limits to infinity are the horizontal asymptotes?! " Well, almost. If the Denom is a higher power than the Numerator then the horizontal asymptotes will be at Y = 0. If the Num and Denom powers are the same, then the Horz Asymptotes will be at the Fraction described by the leading coefficients. But if the Rational Expression is TOP Heavy, that is, if the Num out powers the Denom then you WON'T get a Horizontal Asymptote. There you have to Simplify your Leading Terms of both the Num and Denom and see what kind of Waveform that gives you (if the difference between the Powers is 1, you will get a Straight Line with a Slope, if the difference is 2, you will get a Parabola, etc.)
Thank you Nancy your a blessing we are so lucky to have you...Like SERIOUSLY
Hi @NancyPi thanks for ur outstanding videos. Can you explain Continuity of functions under the topic Limits n Continuity. Thanks in Advance 😊
She just summarized 2 two hours lecture in the most effective way possible 👽
Honestly we need more teachers like this in the world
At first I was like "oh so im gonna learn calculus" but it turns out "oh I think im inlove"
She's gorgeous!
Finally found a video that relaxes you and gives you a headache at the same time :D
i really love the way NANCY explains
..... explains what?!
CREEP
You're amazing! I wish my calculus professor taught like this.
i have a midterm tmrw, and limits is probably going to be on it. i was really stressed bc my professor sucks and i teach myself all the lessons from the book but even then i have questions. so thank you so much for your videos, i really appreciate your time. i also think im going to not do too well on it, and im scared that ill have to change my major., but thank you so much for your help.
update: i passed the class with a B+ 🙌🏽
Nancy, you are a godsend. I'm taking Analysis of Algorithms and have completely forgotten how to evaluate limits until now. Thank you!
Honestly, you have amazing content. Just keep it up
Thank you sooo much for this!!! My teacher is terrible and has no idea how to explain things to us. I always end up having to go to someone like you to figure it out! 😂
Give this women nobel prize pls
welcome back
Your tutorials are the best.
Thank you so much .
This made limits a lot easier to understand. Appreciate it.
Your videos are perfect to review before a test. Thank you so much :')
mommy
im sorry
Nancy thank you for your explanation, really you are a good teacher
Nancy yo are so beautiful i will follow you to the Infinity. ♥♥♥
Geekin
simp
🤣🤣🤣🤣
Thank you, Nancy!
Your explanation makes things easier!
*realizing I'm understanding this*
"Hey, cool!"
*realizing one third of the way through the video that she's having to calculate all of this backwards on the board*
._.
I'm pretty sure she writes normally then just flips the video in a video editor
You teaches always adorably
Thanks again Nancy! I always like how you simplify everything.
Thank you nancy, your help me a lot. God bless you for your reference
You have really cleared my confusion.. please never stop making these videos...you are helping the confused souls in class make it!!!!
Thank you, Nancy! You make my life easier
I really appreciate the great structure you design to elaborate on this! it makes things more clear for me to understand.
Nancy you are my hero !
Hey!! I noticed a thing. Her facial expressions are a lot similar to Dina fitz titan. From attack on titan.
😶😐😐😐😶😶
You're a life saver. Thank you so much for your content.
Nancy is back! Yay!
Thanks you for your videos. It is really helpful for me as well as for the others.
I love how u explain things!
ow..thanks for the basic of limit..hoping for more from u😍😍😍
Really curious how she writes in reverse, or is she? someone explain pls
Right handed, normally, on glass facing a camera on the other side. Then just flip left/right like a lot of webcams do anyway. The fade-out effect of just the text is a little more complicated but I figure out at least one way she might be using.
Was x approaching infinity or was infinity approaching x? Comes to mind here pertaining to my 11th grade 11th grade experience presentation here on youtube. Terrill TC!
Thank you so much, you are just amazing - I'm always blown away by how incredibly simple you present these topics.
Excellent! I love your videos. Thanks for sharing with us your knowledge.
I missed you math queen
You are a very great teacher 'WOW'
I'll be thanking you during my speech at my grad party
Dont worry NancyPi... No one is thinking dirty when you say HUGE, Large, or big..... buuuuuuuuuut the hand gestures on the other hand.... lol those probably more so...... it was rather quite cute watching you holding back your laugh. But thank you for the video it helped me find a answer to my problem.... along with some entertainment.
It really helps a lot when the who teaches is cute.
Please also upload Linear algebra and optimization lessons for graduate students.
Nancy :-| You are so distracting :*
me too... i can't focus... i tried my best to focus but she's so gorgeous but we're grateful for the tutorials :*
yeah but in a good way :D
Unless you love mathematics more than girls