Limits at Infinity (Rational square-root function as x approaches negative Infinity)

In this video I explained how to use the negative sign when x approaches negative infinity. i got a copyright claim on the old music I used. I am working on cleaning it up.
Watch this newer version
• Limit at infinity (of ...

[@PrimeNewtons]

Watch my NEW VIDEO on this topic now kzbin.info/www/bejne/i3OzYnqujt17grs

[@madlad1.]

“Those that have stopped learning have stopped living” what a man, a true academic, great video. Well explained

[@PrimeNewtons]

Thank you!

[@pelasgeuspelasgeus4634]

Are you also presenting and commenting???

[@brianmclogan]

get it!

[@PrimeNewtons]

It's an honor to have you even watch my video. You are a legend.

[@inexp1]

@@PrimeNewtons so amazing! :D

[@LeNguyen-im8dm]

Brain McLogan is my favorite one for graphing trig function.

[@owoshiroi9874]

Thank you!! I feel like I am in a face-to-face class during this video ^^

[@PrimeNewtons]

Thank you. I am glad it helped.

[@PrimeNewtons]

Be careful! This explanation is relevant to Radical expressions containing exponents that are odd multiples of 2 (for example x^6, x^10, x^14 , etc.). If the highest exponent of the argument of the radical was an even multiple of 2 (for example x^4, x^8, etc.) , the negative will be irrelevant and the limit will be positive. I will provide another video to explain this.

[@feedersinternational9895]

Hey boy, where are you from?

[@odgarig8601]

So x^2 is an odd multiple? since its 2x1 and 1 is odd.

[@FinBoyXD]

@@odgarig8601 Yes, 1 is odd, so 2*1 is odd multiple of 2 (x^2), 2*2 is even multiple of 2 (x^4), and 2*3 is again odd (x^6) etc. But this is the squared version already. The original was x^3, and here the exponent needs to be odd for the video to be correct and the negative sign to be added. It only works for odd multiples of 2 because when you turn the x^3 into a square root of a square, you actually need absolute value signs around x^3 to do that. And since because x^3 is negative when x approaches negative infinity the |x^3| is -x^3 , and therefore x^3 = -|x^3|, which then you can square and square root, having x^3 = -|x^3| = -sqrt((x^3)^2) = -sqrt(x^6). But if you have even exponent (which when squared will be even multiple of 2), like x^4, it doesn't introduce the negative sign, because x^4 is still positive when x approaches negative infinity. Then you can just take the absolute value, and square and square root: x^4 = |x^4| = sqrt((x^4)^2) = sqrt(x^8).

[@MinecraftMaster247]

Dude i love your teaching enthusiasm, could you teach more calc stuff? im doing calc right now!

[@PrimeNewtons]

I will like suggested problems to do videos on. Thank you.

[@dariusnuah4125]

Great brother

[@dionys47]

'it will never reach -3, but some day maybe will" that was great man....

[@PrimeNewtons]

I can't believe I said that. ROTF

[@mazenmohsen3423]

*tl;dr* you need to know how to use sqrt() to solve this.

[@omerbayrak-ll7bq]

I am 36 years old and learned limits 20 years ago. I started another major and this gentleman is my hero now. Thank You Very Much. What a nice man.

[@chukwudisimere8463]

amazing video. So i'm doing a math major i really have a particular question question i need an explanation for. is there a way to send the question?

[@PrimeNewtons]

[e-mail]

[@cyvizar]

Excellent teaching! Thank you very much :)

[@gatorscoops3861]

*goose holding knife* "the positive was never an option!" (this is a meme reference so you either know it or you don't :] )

[@kautsariqbal8968]

I'm from Indonesia, thank you, this video helped me a lot!!!!!!,

[@PrimeNewtons]

Glad it helped!

[@khusanakramkhodjaev5583]

Thank you very much! I completely forgot about why we add "-" sign before the square root

[@PrimeNewtons]

Glad it helped!

[@drakem4561]

I have been taking online calculus for the past month and have understood absolutely nothing, but stumbling across this video was the best thing that's ever happened to me this whole semester! Doing a similar problem along with your video for once made me feel like I could solve a problem without resorting to an online calculator. You've got a natural teaching talent, keep on inspiring people!

[@phi1688]

ikr he's amazing

[@Benjamin7534]

Thank you so much I really appreciate this and you. This video really helped me understand.

[@muhammadnajmuddinfarid9567]

Thank you so much, this help me and I like the way how you explain it, it is somehow funny xD

[@PrimeNewtons]

Glad it helped!

[@nsa_2876]

Student from Canada here. Thank you so much for this. You're a lifesaver. You put it in terms I could understand and now it all makes sense to me. Thank you so much.

[@PrimeNewtons]

Happy to help!

[@anujkr.sharma9374]

Dude i love your teaching style btw love from India

[@apothe6]

You are a really good teacher. Most teacher skim over the small bits that can lead students astray, but you cover them

[@Tee0313]

indeed

[@heyzhchenle]

Thank you. I finally got to know what to do to answer number 8 in my quiz lol....

[@anikafabian]

Thank you so much for this!! it really helped clear things up for me !! 🤍

[@Josh-dp6iu]

What would you do if the rational is in the denominator

[@PrimeNewtons]

The denominator is the focus. You must divide by the highest power of x that will eliminate the highest term in the denominator. So, if this expression was flipped, you will still have to divide by x^3 since it works for both numerator and denominator. remember, the focus is on the denominator.

[@saadawan661]

Thank you so much! Teachers like you actually make me want to learn!

[@PrimeNewtons]

Happy to help!

[@forevermore1851]

Thank you so much!! This video was so amazing; I finally understand this!!!!!!!!

[@PrimeNewtons]

Thank you. I am glad I could help.

[@charlesjdan7250]

I should've watched this before reading my module for freaking 2 hours and still not learning anything, like for real bro thank you

[@PrimeNewtons]

I am glad his video was helpful

[@arfsz]

I always found problems like these confusing, but then you explained it so well. thank you so much keep up the great work man

[@jumpman8282]

5:30 As 𝑥 approaches −∞, 𝑥³ also approaches −∞. This means that in this scenario, 𝑥³ is negative. But when we square it, it becomes positive, so we have to write 𝑥³ = −√(𝑥⁶) Thus, lim 𝑥→−∞ (√(9𝑥⁶ − 𝑥) ∕ 𝑥³) ∕ ((𝑥³ + 6) ∕ 𝑥³) = lim 𝑥→−∞ (√(9𝑥⁶ − 𝑥) ∕ (−√(𝑥⁶)) ∕ ((𝑥³ + 6) ∕ 𝑥³) As we "push" √(𝑥⁶) into the other square root, as well as break up the rational expression in the denominator, we get lim 𝑥→−∞ −√(9 − 1 ∕ 𝑥⁵) ∕ (1 + 6 ∕ 𝑥³) Then substituting −∞ for 𝑥, we get −√(9 − 0) ∕ (1 + 0), which simplifies to −3.

[@faustbenj2968]

You seems to be a positive person. very entertaining. pls don't stop making videos. I learned so well from you

[@PrimeNewtons]

Thank you.

[@muhammedaminjeng4269]

Please solve: lim x-> -ve infinity of the function ( sq root of 3x to the forth + 8. Divided by x squared minus 8

[@PrimeNewtons]

lim x-> -infinity [ Sqrt (3x^4 +8)]/(x^2 -8) if you divide the numerator and denominator by x^2 -sqrt 3

[@kamogelomathabathe9761]

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[@wardaulhasan8969]

Great explanation thankyouuu

[@PrimeNewtons]

Glad it was helpful!

[@jasonjocelynchannel7809]

If the graph for that limit approaches -3, what if x=-(6)⅓? Wouldn't it be undefined? The line for the graph (forgot what its called) pauses at before -(6)⅓ and continues after -(6)⅓, so the line can't be continous like what you showed. Good explanation tho.

[@hardeepkour9800]

Thank you so much sir lots of love from india

[@noori6982]

Thank you so much!! Very easy to understand and follow along, and I love your passion/attitude when it comes to math! It makes me feel like I can always work my way through a problem to find an answer, rather than get frustrated and give up on it. Thank you!

[@PrimeNewtons]

Your comment just made my morning. Thank you.

[@danielhester9575]

you gained yourself a sub sir, have a great day

[@zor2014]

time to learn math from a black guy i guess lol- family guy please im black just had to say it

[@PrimeNewtons]

It doesn't matter to me. What matters is that we Never Stop Learning

[@stephaniewabi305]

Wow!! Now I finally get it! You are a God-send! Thank you so much!!

[@PrimeNewtons]

Glad I could help! lol

[@grimfaith8754]

thanks this helped out a lot, loved how you broke it down

[@Bl4ckinferno178]

thanks! this video was super helpful in helping me find out that you need to keep the - sign when you cancel x inside the square root! thank you so much, I was stuck before finding this video

[@PrimeNewtons]

Glad it helped!

[@weggquiz]

thanks so much for an amazing lesson

[@Sesameseedss]

I cannot express how grateful I am that I found this video!!! you truly saved my calc grade sir!!!!!

[@PrimeNewtons]

I’m glad it helped. Thank you for the kind comment.

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Thank you, this is helped a lot since school is online this year due to COVID 19

[@PrimeNewtons]

Glad it helped

[@karayaqubdaffeh3825]

keep uploading more videos of calculus you are just a great

[@hannagrantoza786]

Thank you for your video. I'm struggling with limits so i really appreciate this

[@PrimeNewtons]

Hey Hanna, If there is any question or topic you need help with just email it to me. I can help with a video or a quick reply.

[@hannagrantoza786]

Hello thank you so much! But what is your email? I couldn't find it in the description

[@PrimeNewtons]

@@hannagrantoza786 [e-mail]

[@lenniejoaquin7091]

This was so helpful! Thank you!

[@PrimeNewtons]

Glad it was helpful!

[@user-galactic-nimrod-1]

You're a real life savior man! I have test in 10minutes and online learning is hard but with people like you it's all possible.

[@aneenajoseph8716]

This really helped! Thank you so much!

[@PrimeNewtons]

You're welcome!

[@Idontlikebeingontheibternet]

Thank you for this video! You're an exceptional teacher. Keep making videos!!

[@kiddcamel]

Wow. I was so confused when my prof randomly made the numerator negative, and after a poor explanation I felt lost. Same with the dividing in to the bracket. You explained it clearly in 8 minutes. Thank you.

[@PrimeNewtons]

I'm glad it helped

[@znhait]

When it comes to limits--especially before doing any derivatives--this sort of problem and the ones with one-sided limits require more than just plugging in values and getting a number. It requires some thinking on the student's part. For these sorts of problems, particularly the one worked out in this video, I would always suggest to do a quick check before starting. And that would be to check the sign of the leading term as x gets very large--in this case, negatively large--to see what the sign of the answer should be.

[@xavierwarren9799]

Love your teaching style bra...keep going.

[@alimaisamamiri2530]

I was having problems understanding the signs when we take the roots when x goes to infinity.

[@hasandaone3815]

i am from iraq and you dont know how much you helped me , thanks teacher

[@PrimeNewtons]

I am glad I could help.

[@swenpai]

This was very helpful, thank you very very much! 💓

[@FrancisFaithman]

wow, i amazed at how you teach. You are one of the clearest teachers i have ever met. You explain every step into detail. Thank you so much

[@zakiatabassum9549]

This was explained beautifully! You need more views

[@PrimeNewtons]

Thanks

[@c4rlo237]

Can I ask why do yung divide with x³ instead of x^6??

[@PrimeNewtons]

You MUST only focus on the denominator. Always divide by the highest power of x in the DENOMINATOR. Remember that ALWAYS. By doing this, you will eliminate any possibility of getting an undefined expression except when the limit is actually infinity.

[@naomkerubo5109]

Wow you're the best teacher I've met online you have really made it simpler for me, thank you God bless you to continue with the same spirit

[@PrimeNewtons]

Wow, thank you!

[@kizamesakazuki3734]

u are so amazing honestly its ur first video I watched and I learned so much like the absolute value I used to square -2 and I forget the negative sign

[@PrimeNewtons]

Thank you for the kind words

[@carllesterocampo1856]

This is so effective bro I literally get it in here than in our calculus

[@karimabouelela3665]

keep it up, I like you cus syou bring hard problems

[@PrimeNewtons]

I appreciate that

[@yhangwiththeh]

Thank you, Sir! You remind me of my Math teacher.

[@FirstnameLastname-ik5fo]

This video has helped me a lot. After a long time it finally clicked after watching your video especially with the negative sign. Thanks!

[@Raphael-bq1fc]

exactly the explanation i was looking for

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Very well explanation, love it..❤❤ God bless.🙏

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Thank you for doing this, you don't know how much it means to people that are trying to their best to study and have a full time job, We really appreciate it.

[@PrimeNewtons]

I am glad it helped

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Another excellent video helping so many students! 👍

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I'm from Ethiopia thank you this video is help me

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i needed this so much! thank you for saving my life! greetings from the Philippines:))

[@armaanbranudeen5117]

Thank you very much sir. You cleared my doubts

[@sherry3501]

hi sir! thank you so much for this amazing video. I finally understand how to solve problems like this now. And you also answered all the questions I had in my head which is so crazy. Officially subscribed, thanks again for your help!

[@LeNguyen-im8dm]

What is beyond excellent? it is Prime Newtons.

[@jochemkralt]

The first video I find that addresses this type of limit and it is absolutely amazing, never seen someone explain math so well and with such positive energy

[@elmariajin744]

I loved your video. The way you kept smiling and said things with fun expressions, made me enjoy watching this video and learning about limits.

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Will Smith doing Calculus! I love this channel.

[@nightrider7320]

Best explanation💝❤

[@AaLl-fe9ix]

5:38 I have a calculus final exam tomorrow! My professor indeed says that I can't forget to write the following in between my steps for solving the problems: "Limit" sign "Integral" sign with a "dx" or "d" with a variable that I am integrating/taking the antiderivative of "+ C" at the end of my answer with the antiderivative. If I'm taking the antiderivative of "1 / x", then it needs to be "ln(|nx|) + C)" -- I don't think that he told me that I should write the "n" in the natural log, but I will just in case, and the number/variable "n" represents another constant/number. And the reason why the antiderivative of "1/x" is "ln(|nx|) + C" is because if we take the derivative of "ln(x)" we will get 1 / x, but if we take the derivative of "ln(nx)" while "n" is another number, then we will also get "1 / x", but either the chain rule, or using the "log of product = sum of logs" rule, knowing that we will get "d/dx (ln(nx)) = d/dx (ln(n) + ln(x)) = d/dx (ln(x)) = 1 / x". I just want to write the answer as "ln(|nx|)" to be on the safe side!

[@PrimeNewtons]

Your professor is right. Please do as advised.

[@ahmadfarizuddinbinmohdaidi9431]

thank you man..finally i understand the topic well

[@GEETAgeeta-ex9cd]

AMAZING👍👍

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Thank you, I use videos to help me understand my math homework outside of class, I watched multiple videos before this that wasn't helping me understand how to do the problems. Glad I found yours!

[@PrimeNewtons]

I'm glad you find them helpful

[@SuhelHasnein]

Thank you for the explanation,ur the best! ❤

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Keep flying brother!,you're a indeed a gift to us.

[@PrimeNewtons]

Thank you, brother

[@emmanuelpaygar3736]

Wow! Thanks for the nice explaination.

[@kobsylvester327]

This video is really good. Great job Newton

[@Chip4576]

Can you not just multiply by the conjugate?

[@PrimeNewtons]

The Radical then move to the denominator and the problem will remain and even get worse.

[@Prime94510]

Why aren't you my teacher 😭?

[@PrimeNewtons]

Lol!

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you are a great teacher!

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we love you prime newtons

[@PrimeNewtons]

I love you too!

[@elijahromero5684]

This is exactly what I needed. Thank you so much.

[@Sean-dm8ez]

This video was the key to me solving a very complex problem on a calculus exam, thank so much :)

[@PrimeNewtons]

Glad it helped!

[@dhlsttm348]

The last part you said, actually hit me. Thank you! You don't know how much it means to me to hear that, maybe someday, I can finally get that -3! T^T.

[@PrimeNewtons]

Wow! Thank you for the positive feedback. I appreciate it and I’m glad you learned something.

[@dalya.mohammed]

Thank you so much

[@absolutezc8116]

Thank you so much helped a million

[@edubblesspirit]

I can’t believe in all my algebra years I never learned that technique of putting a term back inside the square root. Thanks

[@PrimeNewtons]

Glad you haven't stopped learning.

[@theowilliamson5692]

That was a smooth outro haha. Thanks for the help!

[@PrimeNewtons]

Glad it helped!

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This is || absolutely the best math explanation video I have ever watched, I don't understand why it isn't always taught in common language like this, you have earned my subscription.

[@PrimeNewtons]

Wow! That is a great compliment! Thank you!

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Thank you sir

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Thank you from the depth of my hurt. Carry on 😊

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I enjoyed your teaching thank you sir