Limits at infinity can be a hard subject to grasp, but you do an amazing job of explaining it. I thoroughly enjoyed watching this video and even caught myself smiling with you. Thank you for loving what you do and sharing it with the world!
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.
@@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).
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!
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.
I just found this channel and I swear that the moment I saw this guy's face I was like: omg that's a good person! We really do need nice people like him around....
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
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.
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.
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.
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!
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.
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
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!
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
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.
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.
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!
Math major student from Philippines here, thank you so much for your thorough discussion, it is way easier to comprehend. I love to learn more about your teaching esp. in calculus and I am hopeful that you will help me. Ty
Wow that was crystal clear. Not only that you have a really great charisma and that makes whatever you teach more credible to students. Thank you and good day :)
I am so guilty about this, because I always forgot that there are 2 signs to consider in finding suareroots, it is either + or - , thank you so much sir ❤❤❤
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“Those that have stopped learning have stopped living” what a man, a true academic, great video. Well explained
Thank you!
Are you also presenting and commenting???
'it will never reach -3, but some day maybe will" that was great man....
I can't believe I said that. ROTF
@@PrimeNewtons what if there are root squares on up and bottom
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.
Limits at infinity can be a hard subject to grasp, but you do an amazing job of explaining it. I thoroughly enjoyed watching this video and even caught myself smiling with you. Thank you for loving what you do and sharing it with the world!
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.
Hey boy, where are you from?
So x^2 is an odd multiple? since its 2x1 and 1 is odd.
@@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).
get it!
It's an honor to have you even watch my video. You are a legend.
@@PrimeNewtons so amazing! :D
Brain McLogan is my favorite one for graphing trig function.
Thank you!! I feel like I am in a face-to-face class during this video ^^
Thank you. I am glad it helped.
You are a really good teacher. Most teacher skim over the small bits that can lead students astray, but you cover them
indeed
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
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!
ikr he's amazing
The most iconic thing is, taking about the main part at the beginning. It will save others time a lot. Thank you
I like iconic levels.
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.
Happy to help!
I just found this channel and I swear that the moment I saw this guy's face I was like: omg that's a good person!
We really do need nice people like him around....
Only a good person thinks another is good. I am honored to get such assessment from you. Thank you.
@@PrimeNewtons no, thank you! Please keep it up with the good work, ur AMAZING 👏
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.
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
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.
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.
I'm glad it helped
Thank you so much! Teachers like you actually make me want to learn!
Happy to help!
I cannot express how grateful I am that I found this video!!! you truly saved my calc grade sir!!!!!
I’m glad it helped. Thank you for the kind comment.
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.
I should've watched this before reading my module for freaking 2 hours and still not learning anything, like for real bro thank you
I am glad his video was helpful
I can’t believe in all my algebra years I never learned that technique of putting a term back inside the square root.
Thanks
Glad you haven't stopped learning.
You seems to be a positive person. very entertaining. pls don't stop making videos. I learned so well from you
Thank you.
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.
I am glad it helped
By far the greatest explanation I have watched regarding this topic.
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
Wow, thank you!
i am from iraq and you dont know how much you helped me ,
thanks teacher
I am glad I could help.
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!
Your comment just made my morning. Thank you.
This video has helped me a lot. After a long time it finally clicked after watching your video especially with the negative sign. Thanks!
This was the most clear math video I have ever seen. Please make more videos !!!!!!!
I wish all my teachers started off their lectures with a smile like his
Dude i love your teaching style btw love from India
You are the best teacher ever on youtube! Thank you!!!
Wow, thank you!
I always found problems like these confusing, but then you explained it so well. thank you so much keep up the great work man
I had a huge blocker with the idea of when we are supposed to divide by a negative x versus not. This really helped. Thank you!
Keep flying brother!,you're a indeed a gift to us.
Thank you, brother
This was explained beautifully! You need more views
Thanks
Love this!! Very nicely done and explained. When people smile while doing math, well, it just makes it so much more engaging and fun. Thank you!
very true
MY GOD!!!!! THIS IS THE VIDEO I'VE BEEN LOOKING FOR!!!!!
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.
Wow! That is a great compliment! Thank you!
This is so effective bro I literally get it in here than in our calculus
concise, clear and quick. This is an absolute banger of a video!
Dude i love your teaching enthusiasm, could you teach more calc stuff? im doing calc right now!
I will like suggested problems to do videos on. Thank you.
Great brother
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
Thank you for the kind words
i absolutely love you energy it makes the video enjoyable and more understandable keep on posting ,this is very useful
thanks this helped out a lot, loved how you broke it down
Love your teaching style bra...keep going.
You're an absolute godsend! Thanks to you I will ace my calc finals tomorrow! Thank you brother :)
You can do it!
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!
I'm glad you find them helpful
exactly the explanation i was looking for
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
Glad it helped!
Wow!! Now I finally get it! You are a God-send! Thank you so much!!
Glad I could help! lol
I'm from Indonesia, thank you, this video helped me a lot!!!!!!,
Glad it helped!
The video was very good! Really helped me understand how x is a negative number in the limit. Thank you!
You're very welcome!
This video was the key to me solving a very complex problem on a calculus exam, thank so much :)
Glad it helped!
Excellent teaching! Thank you very much :)
Thank you! This helped me solve a problem I’ve been stuck on for hours!
Thank you very much! I completely forgot about why we add "-" sign before the square root
Glad it helped!
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.
Wow! Thank you for the positive feedback. I appreciate it and I’m glad you learned something.
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.
I love your enthusiasm. Never stop learning and god bless.
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!
Your professor is right. Please do as advised.
Teaching style is damn amazing and you made me understand the concept so amazingly well...
Thank you for your video. I'm struggling with limits so i really appreciate this
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.
Hello thank you so much! But what is your email? I couldn't find it in the description
@@hannagrantoza786 primenewtons@gmail.com
Thanks. Was stuck for long time. Good concise explanation.
Math major student from Philippines here, thank you so much for your thorough discussion, it is way easier to comprehend. I love to learn more about your teaching esp. in calculus and I am hopeful that you will help me. Ty
you gained yourself a sub sir, have a great day
Honestly wanna say that i like your teaching method:)
Wow that was crystal clear. Not only that you have a really great charisma and that makes whatever you teach more credible to students. Thank you and good day :)
Glad it was helpful!
I am so guilty about this, because I always forgot that there are 2 signs to consider in finding suareroots, it is either + or - , thank you so much sir ❤❤❤
I search this topic and hopefully I understand this by u!
Thanks man❤️❤️
Thank you so much I really appreciate this and you. This video really helped me understand.
i needed this so much! thank you for saving my life! greetings from the Philippines:))
Another excellent video helping so many students! 👍
Thank you for this video! You're an exceptional teacher. Keep making videos!!
Oh man What an excellent style of teaching Thanks❣
Thank you so much, your teaching is very intuitive!
Maaaan your are a great tutor, Thank you 👍🏾👍🏾👍🏾
Thank you. I’m happy you found it helpful
I love your shirt man, it matches with the entire session video. Great way, for visual learner and autistic.
This video is really good. Great job Newton
Thank you, Sir! You remind me of my Math teacher.
*goose holding knife* "the positive was never an option!"
(this is a meme reference so you either know it or you don't :] )
This is exactly what I needed. Thank you so much.
Thank you so much for this!! it really helped clear things up for me !! 🤍
great video! I had trouble figuring out how to sneak the high power into the root! and you helped me a lot
This was great. Thanks a lot mahn. This has saved me a ton of hours of learning. Keep Learning!!!
you are a great teacher!
keep uploading more videos of calculus you are just a great
Thank you for the explanation you made it very easy to understand 👍
youre so good at teaching!
I appreciate that!
Very well explanation, love it..❤❤ God bless.🙏
Thank you so much! I was stuck on figuring out how to fully simplify with the fractions and radicals.
I'm glad the video helped
YOU ARE A LIFE SAVER!!!!
Lol. I'm glad it helped.
Thank you from the depth of my hurt. Carry on 😊
🥺🥺🥺Best tutorial eveeeeeeeerrrrrrr!!!!!!!!!
Thank you so much! You really made me understand this topic. Love this channel!
Thank you so much sir lots of love from india
Best explanation💝❤
This is a really helpful video thank you for making this easier to understand!