This book was the text used at my college for honors calculus students at my community college. That together with an excellent professor inspired me to be the unemployed mathematician I am today!
@antikertech157 Жыл бұрын
There's many things you can do with mathematics....and monetize.
@esra_erimez Жыл бұрын
"the unemployed mathematician I am today" 🤣
@taekwondotime Жыл бұрын
Well said. The government (at the request of big tech companies like Google) is always pushing people to take more and more math, and to get into STEM fields. Meanwhile the world needs doctors, nurses, and skilled tradespeople.
@taekwondotime Жыл бұрын
@@antikertech157 If you can't build houses, do plumbing, install electrical wiring, do welding, or treat injured/sick people, then you have no skills worth anything.
@antikertech157 Жыл бұрын
@@taekwondotime Jokes on you. I am also a salesman and copywriter, I use the knowledge of probability and statistics in my favour. Furthermore, I use my research skills to analyze the market for a good marketing strategy.
@fernandomejias3854 Жыл бұрын
A classic of all times!! Unfortunally Professor Spivak passed away in 2020. "Calculus", as any other of Spivak's books is a real gem!
@LucasDimoveo Жыл бұрын
This book seems like a bridge to an intro Analysis course. I purchased it to start learning Analysis while keeping my computational Calc skills sharp
@21ruevictorhugo Жыл бұрын
I absolutely love this book. I learned math in a sort of backwards way, since I was a part time student and part time courses were very limited, but the math department decided I could just take whatever course I wanted as directed study - pick a book, no classes, no lectures, just read and come and ask questions. I started with abstract algebra and absolutely loved writing proofs. I then took a summer course in calculus - two weeks of all day classes. (That was my vacation from my job.🤣)Talk about cramming. I barely passed it. Then I did directed study with this book and loved it because abstract algebra and topology were all about writing proofs, so this book was exactly what I was used to.
@dalitlegreenfuzzyman Жыл бұрын
One of the best books ever written. No hyperbole. It’s truly a piece of art.
@markcassidy2410 Жыл бұрын
I love this book. I used it to study/learn calculus on my own during one summer. The problems are hard. The text and approach are excellent. Really turned me onto math with its rigor.
@scienceskills Жыл бұрын
Ciao ! Spivak's Calculus is an amazing book. The depth with which he explains concepts is impressive. That's a real math textbook that mitigates the churn-and-chug approach of many students.
@TheMathSorcerer Жыл бұрын
Couldn't agree more!
@akshaylenin71668 ай бұрын
In order to understand proofs and theoretical Mathematics, you need to have a large number of examples and do abundant computational style questions to understand the patterns
@UnconventionalReasoning8 ай бұрын
What concepts need to be explained in depth?
@UnconventionalReasoning8 ай бұрын
@@akshaylenin7166 Or the learner can read about the relationships and identify the patterns from that. Doing abundant computational style questions is extremely ineffective and inefficient.
@akshaylenin71668 ай бұрын
@@UnconventionalReasoning both problems and practising Theorem proofs go hand in hand for better effectiveness
@sergeydukman5832 Жыл бұрын
"That is crazy. Totally nuts" - exact thoughts of mine when I don't understand math
@AnthonyLauder Жыл бұрын
Spivak passed away in 2020, when he was 80 years old.
@TheMathSorcerer Жыл бұрын
wow
@meteor8076 Жыл бұрын
yep, thats sad (
@josepereira2759 Жыл бұрын
One great book from spivak is "calculus on manifolds". I ve used it on my "calculus 3" classes
@jksmusicstudio1439 Жыл бұрын
I remember myself at first year of uni trying to understand the ε,δ definition of limits. I was stuck for about a month on the fifth chapter, reading again and again the explanations. I dont think that any other book would make it as clear as this one did. Definately one of the best introductory texts to advanced mathematics.
@maximofeliz7324 Жыл бұрын
May this book be compared to this other vintage Book: calculus by Granville.?
Haven't tried Spivak, but I found Thomas's limit chapter to be very good.
@ai_serf Жыл бұрын
When looking to get into analysis and develop a rigorous understanding of Calculus, I found 3 books always recommended: Spivak, Rudin and Apostol. I went with Apostol which I'm in love with; but if I had one extra life, I'd also like to spend the thousand or so hours I would take to go through every problem in Rudin and Spivak's Calculus books.
@jesusandrade1378 Жыл бұрын
Spivak's Calculus Fourth edition differs from the third mainly in the inclusion of additional problems, as well as a complete update of the Suggested Reading, together with some changes of exposition, mainly in Chapters 5 and 20.
@TheMathSorcerer Жыл бұрын
Excellent thank you for this comment!!
@Dhruba-t7n4 ай бұрын
which one should i buy
@fmeyer_ Жыл бұрын
Spivak and Apostol live rent free on the back of my mind.
@johnnath4137 Жыл бұрын
Looking at your post brings to mind two interesting texts which I learned my analysis from in my youth. They were both originally published in German, and were later translated into English, which were the text I used. The author was the great German number theorist Edmund Landau (not the Russian Physicist L D Landau), who was originally a student’s of Frobenius (the mathematician who gave the first general proof of the Cayley-Hamilton theorem), with whom he did not get on, and later a student of Hilbert’s. Landau later went on to become one of the founding members of the Hebrew university, Jerusalem, and one of its leading lights. The two texts went by the titles Foundations of Analysis and Differential and Integral Calculus. The former gave a construction of the real number system from a simple postulate system for the natural numbers and naïve set theory and the second gave a rigorous development of the main theorems of the calculus. The text was severe in its approach to rigour - Landau boasted that you would find a single diagram in it. And the second theorem, after the definition of the derivative, was a proof of the existence of an everywhere-continuous-nowhere-differentiable function. I still have my copies of both texts, and I prize them. At high school I was introduced to rigorous calculus by a teacher’s lending me his copy of G H Hardy’s Pure Mathematics, at the time a seminal analysis text in English. At the time I had a lot of difficulty understanding irrational numbers - my problem was that they didn’t make any sense whatever. Hardy helped me resolve most of my difficulties. The two Landau texts removed them all. Alas! by that time I had already left high school..
@akshaylenin71668 ай бұрын
Srinivasa Ramanujan Sir did his research under Prof G H Hardy
@johnnath41378 ай бұрын
@@akshaylenin7166 Yes, but everybody knows that. What's your point?
@akshaylenin71668 ай бұрын
@@johnnath4137 my point is that Srinivasa Ramanujan Sir had such superhuman intelligence to immediately grasp and drink those complicated Mathematical concepts without the help of a teacher which proves that a good guide book is equally powerful to understand complex concepts in simple way.Moreover, Srinivasa Ramanujan Sir is actually a higher dimensional being like Gauss, Euler,Cauchy, etc
@akshaylenin71668 ай бұрын
Even to do research on composite numbers under Prof G H Hardy speaks volumes of Ramanujan Sir's brilliance and Calibre
@arantheo8607 Жыл бұрын
A real gem! ( Essential Calculus with Applications, by Richard Silverman, great as well)
@ap3montes739 Жыл бұрын
I tried reading it a while ago. Got to the exercises (those little proofs) in Chapter 1 and got completely stuck. I then decided to sharpen my skills, and began with the "A transition to advanced mathematics" book. I hope that my proof skills are enough by the time I finish it so I can comfortably read Spivak.
@TheMathSorcerer Жыл бұрын
Excellent!
@thiagogalvao223 Жыл бұрын
Hey bro, can you give-me a feedback of your strategy? I mean, have you got the level for follow the book?
@HJohannes93 Жыл бұрын
Great book! Combines conversational and motivating language with hardcore rigour (at least if it's for a first course in calculus). I only studied the first 12 chapters during one of my summer breaks of university, didn't manage to get farther than that... Maybe I'll pick it up again in the future :)
@huiyinghong3073 Жыл бұрын
It still isnt at the Real Analysis level of rigour, more like a baby analysis book
@HJohannes93 Жыл бұрын
@@huiyinghong3073 Of course, it’s still a calculus book but with emphasis on theory, not an analysis book 😊
@huiyinghong3073 Жыл бұрын
@@HJohannes93 In my school at least, the distinction between calculus and analysis is never really so clear cut. They introduce a bit of analysis stuff in calculus courses to year 1 Math students before going full blown analysis in Year 2.
@benhill3098 Жыл бұрын
Late comment here, but the 4th edition and the solutions guide arrived yesterday at my home (October 7 2022). Can't wait to use this as my supplement for calculus next year, along with the books by Stewart, Larson, Thomas, and a bunch of others I have 😄Thanks!
@kray97 Жыл бұрын
First year in college for me. It is a great book, but some of the problems in there are pretty insane. It was also a my first course in proof based mathematics (not counting HS Geometry), and like you, I basically had zero proof writing skills. So this class was a chore and then some for me. Many of the kids in my class did have proof writing skills btw. You didn't learn any of this in AP Calculus.
@user-qj3rv2mo1b8 ай бұрын
I just got calculus by Spivak 3rd edition. The book looks great for someone willing to read cover to cover or use it as reference and not suitable for those who like to learn by grasping concepts delivered through solved examples. This is my first impression about the book.
@maheshpadalingam3137 Жыл бұрын
I think I'm going to buy this after Thomas calculus. Oh, and can you do something like a self study asmr? I always to see more self study content, so that would be really cool to see.
@TheMathSorcerer Жыл бұрын
That's a great idea!
@Singularitarian Жыл бұрын
Great video! I’m such a fan of these book reviews / commentaries.
@QuantumEntanglementForFun Жыл бұрын
I learnt calculus from this book 40 years ago, probably from the first edition. Loved the book but my recollection was the book was much more theoretical with very few practice problems. I remember after taking the course that I could prove derivative/integrals existed but I couldn’t actually do them. I still have the book. I will have to compare this video to my book when I get a chance.
@TheMathSorcerer Жыл бұрын
Thanks for sharing!
@UnconventionalReasoning8 ай бұрын
There are only a dozen derivatives to "actually do".
@QuantumEntanglementForFun8 ай бұрын
@@UnconventionalReasoning I only count nine. Eight from the letters in “actually do”: d(“actually do”)/da = 2“ctually do”, d(“actually do”)/dc = “atually do”, d(“actually do”)/dt = “acually do”, etc. All others are zero: d(“actually do”)/db = 0, d(“actually do”)/de = 0, etc 😁
@AlphaForgeMedia Жыл бұрын
Hi sir I am from India, now I am in High school, in just 4 months i will join college for undergraduate course ,i love your videos ,thanks to spead this valuable knowledge.
@AlphaForgeMedia Жыл бұрын
Thanks for ❤️❤️
@KMMOS1 Жыл бұрын
Note that between pages 619 and 662 in the fourth edition of Spivak's Calculus are answers to selected problems from the text.
@FrancisCWolfe Жыл бұрын
I felt the weak point of this book is the bit about integration by substitution, which didn't make sense to me to the same extent as the rest of the book. I was gratified to find an article by David Gale, "Teaching integration by substitution" which both reassured me that it doesn't sense as presented and explains it properly.
@orestesdd11 ай бұрын
This book by Mr. Spivak was used extensively in my first math semester ever at the university of Havana, and I consider it a math book GOAT!!! However, since I didn't fish my math studies in Cuba but in the US, I used it a lot here although it was never the main textbook at my college in California. 🤔
@zgennaro Жыл бұрын
You might consider George Simmons calc with analytic geometry 2nd edition. Non rigorous but makes everything “very difficult or impossible to doubt”. Has very good exercises that focus on understanding after the computational problems
@TheMathSorcerer Жыл бұрын
Thank you so much!!
@joeaverage8329 Жыл бұрын
Very good author/mathematician indeed. Love his DE book.
@azimuth4850 Жыл бұрын
Hey Math Sorcerer. Just wanted to tell you that my copy of Higher Algebra arrived today and it smells aaaaamazing! It smells like an old library. 😃😀🙃
@TheMathSorcerer Жыл бұрын
Oooh NICE!!!!!!!!!
@azimuth4850 Жыл бұрын
@@TheMathSorcerer Yeah man!! lol 🤣 Keep it up, you are awesome!
@ANTGPRO Жыл бұрын
I like pretty much your books overview.
@peterhi503 Жыл бұрын
Could you please do a video comparing Spivak and Apostol?
@mohamedmounir6770 Жыл бұрын
I think this is the calculus book 📖 for the simple meaningful words and the way you get the information either you're a math major student or simple person who get interested in calculus.
@granteckhardt4878 Жыл бұрын
8:22 made me chuckle. I said wow twice just as you did haha!
@Apuryo Жыл бұрын
Is there a multivariable calculus book with the same approach like this book? I have been doing Spivak for a while and want to have some practice with 3d+. Do you think Buck's advanced calculus or Loomis calculus would be good?
@jotteria79 Жыл бұрын
on page 247, exercise 12-8 ("...lacking a car, bicycle, or trusting friend...") was just needlessly cruel lol
@jadeharley413 Жыл бұрын
BRO I WAS JUST READING THAT EXERCISE LMAO
@maccleary9576 Жыл бұрын
Looks cool, I'm not fully at that level yet, I have only just started doing calculus. I'm taking the Neil DeGrasse Tyson approach of letting the cloud and fog clear as time goes on, ie. just sticking at it. The good thing about math is that it is precept upon precept.
@hatemalkd1633 Жыл бұрын
I hope in some day see your book And guess it will be brilliant book I don't know but I guess it will be about calculus because I saw you interested so much at calculus Good luck for you
@billmorrigan386 Жыл бұрын
Yeah, this is a superb very advanced book on the single variable calculus. Inclusion of the proof for the irrationality of pi is really commendable as are numerous challenging problems with asterisks. In comparison with standard books, the challenge problems in this books are way harder. What's more, most people might find standard Spivak's problems (with no asterisks) already very challenging.
@luigiguilli9346 Жыл бұрын
My undergrad school used this also for their honors calc sequence at University of Rochester.
@TheMathSorcerer Жыл бұрын
Oh wow that's pretty cool.
@BBVictini1 Жыл бұрын
Ayy fellow UR student!
@slowjazz5932 Жыл бұрын
I asked you about this book a few videos ago. I like to think that I caused you to talk about it again lol. I encountered this book from going to a certain liberal art college in Florida, they used this book for a class call "Calculus with theory", it's more like baby analysis for freshmen.
@TheMathSorcerer Жыл бұрын
Oh wow that's cool that they used it there.
@thecodingcanuck Жыл бұрын
I absolutely love this book!
@JR-uc3nk Жыл бұрын
The fourth edition exists - I have it, definately excellent!
@satyavivekanandbattula1091 Жыл бұрын
Thank you Sir. Useful video.
@dwdei8815 Жыл бұрын
Funny that you chance upon the Cauchy-Schwarz inequality on p 276 - because Spivak first demands you present a proof of it in ChPater One (Basic Properties of Numbers)! I'm slogging through it untutored, self-learning, and my goodness it's hard going! Some of the formulas like the product and sum ones I treat like mechanisms, each element in them a cog, and I have to write narrative of how they work before I can fully encompass them.
@jostpuur7 ай бұрын
It is extremely common that teaching materials on calculus omit the proofs of the most difficult theorems, and give heuristic justifications only. Does Spivak do the same, or does this book contain serious proofs of the difficult theorems too?
@JohnVKaravitis Жыл бұрын
I had this in high school back in 1980-1981.
@TheMathSorcerer Жыл бұрын
oh wow that's awesome
@daxramdac7194 Жыл бұрын
Those insanely difficult derivatives actually look fairly easy bro, I remember taking calc 1 and, compared with integrals in calc 2 where you had to think and be a little creative, with calc 1 once you found the ultimate pattern of derivatives, it made doing 99% of derivative problems a matter of pattern recognition and careful rule application. The difference between easier and harder derivatives being a test of your patience and attention span.
@tobeornottobehaidar4493 Жыл бұрын
Please make a video about Thomas calculus book twelfth edition....Thank you for your best efforts,I dare to say this channel is the best.
@jesusandrade1378 Жыл бұрын
I think that the 9th Revised edition of 1996 is the best Thomas' Calculus edition, and it was the last edition he himself wrote before passing away. The newer editions were written and adapted by different authors.
@licorice4956 Жыл бұрын
Maybe you could do a video on the famous calculus books(Spivak, Apostol and Courant) and your thoughts on them and their differences. I think you would need to look around for the solutions manual for Courant by Blank on the internet archive, though.
@imdarealani Жыл бұрын
I've considered trying to read this book. I'm still not sure whether I should go for it. Thanks for making a video on it.
@mdmojibar53265 ай бұрын
I like the early trencedentals by james steward
@UnconventionalReasoning8 ай бұрын
For the derivatives shown in chapter 1: "The Chain Rule: One Rule to Rule the Rules".
@FullmetalPain Жыл бұрын
Have you ever read "Measure and Integration Theory" by Heinz Bauer? It's a classic here in Germany and I wonder what you might think of it. Especially compared to something like Donald L. Cohns book.
@TheMathSorcerer Жыл бұрын
I have not, thank you for the suggestion!!
@aigeanthokchom3797 Жыл бұрын
REQUEST FOR MATH BOOK REVIEW: Author Name: Mark Dugopolski, Book: Elementary and Intermediate Algebra, College algebra. Hey math sorcerer, I have been trying to find good books on basic math. Many people suggest me to watch khan academy but I think watching videos is not enough. I watched many of your book reviews and after doing a little research myself, I found these books by Mark Dugopolski. I want to know what you think of them. Thanks.
@Chris_Bonner Жыл бұрын
I just watched your other video on this same book from a few years aho
@Chris_Bonner Жыл бұрын
Years ago*
@Feynman-fj2gr4 ай бұрын
I read it when I 14 was one of my dream solve the problem with two stars
@evaisthisiaeclaire63658 ай бұрын
Could anyone explain why that question 40 is considered hard? Isn't it easily provable using L'Hospital's Rule?
@vegenzohrabian534010 ай бұрын
it is "such a cool book"... great collector item in any lilbrary
@rk99688 Жыл бұрын
You know what is sad that they expect you to learn this stuff with no prior proof experience from high school. Uwaterloo loves to make things harder on purpose.
@lucasbomfim00 Жыл бұрын
It's like when the first thing they talk about programming is recursive functions. Seems like gatekeeping.
@catafest Жыл бұрын
It seems like a very good book, can it be converted into an open-source format like epub? Copyright? There should be no impediments with a scanner, a text converter, and Latex formulas.
@fernandocupil.6463 Жыл бұрын
Estoy apunto de hecharme los dos paquetitos jeje. El libro de Cálculo de Spivak y su solucionario, ya casi junto el dinero :) pero no he encontrado ningún review en KZbin hasta ahora que muestre el solucionario. Espero poder verlo en KZbin antes de poder comprarlos. Saludos :)
@TheMathSorcerer Жыл бұрын
Voy a tratar de hacer un vídeo en el Libro de soluciones. Yo lo tengo aquí. Gracias y saludos!
@jesusandrade1378 Жыл бұрын
Hay un Manual de Soluciones que combina las dos ediciones, Tercera y Cuarta.
@fernandocupil.6463 Жыл бұрын
@@TheMathSorcerer Kheeeeee????? Ya tienes el solucionario???!!!! ME dices que vas a hacer un review!!! Bro vas a ser el primero que emocióoooonnnnn😭😭😍🤩😱😱
@TheMathSorcerer Жыл бұрын
Lo voy hacer ahora mismo
@ADDISONxz Жыл бұрын
I go to the University of Waterloo and unfortunately they no longer use this text (at least in my honours math classes).
@TheMathSorcerer Жыл бұрын
Oh I see, interesting.
@ADDISONxz Жыл бұрын
@@TheMathSorcerer We actually have a lot of textbooks made by professors at UW now. I could send you the electronic copies if you're interested.
@huiyinghong3073 Жыл бұрын
What about Multivariable calculus? Does this book include that as well?
@MarcusAsaro Жыл бұрын
My recollection is it does not.
@aayushvinay1492 Жыл бұрын
I've read this, it's really good 👍
@DropTehBazz Жыл бұрын
Contemplating whether to buy the Apostol Calc. books or this one. How do they compare? (The more thorough the book is the better as far as I'm concerned)
@marcelsmolik9469 Жыл бұрын
Hi great video as always. Do you have some probability/statistics books?
@user-qj3rv2mo1b8 ай бұрын
How about teach calculus by Spivak on KZbin by solving selected problems. Thanks
@SwaIok Жыл бұрын
Sensei your book collection is like a zen garden, peacefully quite and equal parts awesome! Namaste.🥷🥷.
@alvinah830 Жыл бұрын
I love mathmatics but i do not have more book I hope i have this book
@excuilax1325 Жыл бұрын
I really like this book, i've been using it as a supplement for my calculus course.
@florianzellmer8735 Жыл бұрын
Dear Math Sorcerer and community! I am taking an introductory course in numerical mathematics right now, but unfortunately we did not get book recommendations. Can someone help me out finding a good one? Thanks a lot in advance!
@meteor8076 Жыл бұрын
What kind of chat room are you talking about ? is it still active ?
@varungk3388 Жыл бұрын
Please review Richard Courant's Calculus and Mathematical Physics books.
@Jonathan-wo6kf Жыл бұрын
Have you ever heard of the Tau manifesto? It's a pretty compelling argument that tau should replace pi that is fairly convincing. The idea comes from a guy named Michael Hartl if you want to check it out.
@henriquenascimento545110 ай бұрын
Do you know a good book about multivariable calculus with the same style as this one?
@sophiahitch726 Жыл бұрын
I need master sorcerer's guidance to help me in my math battles
@Diaming787 Жыл бұрын
How does it compare to Abbot "Understanding Analysis"?
@michaelsommers2356 Жыл бұрын
Is the yellow pig still in the index?
@kevincline9155 Жыл бұрын
She was fathered by Mike Spivak in a bar across the street With a beauty in her bosom but only sixteen feet Because she was consistent, she could hardly be complete Her proofs go marching on.
@sundaymanali5854 Жыл бұрын
should i read this if i alrdy took calculus?
@dacioferreira7127 Жыл бұрын
Are this book or Apostol's book better?
@user-yp6ze3dh5j Жыл бұрын
The way I learn English ☺
@TheMathSorcerer Жыл бұрын
Oh that's awesome!
@WaelAjam Жыл бұрын
Please math sorcerer what are the standard textbooks for the undergraduate math majors in the US?
@TheMathSorcerer Жыл бұрын
For Calculus something like the book by Stewart or the one by Larson is very standard.
@canusakommando9692 Жыл бұрын
Waterloo is an excellent school.
@sloppycee9 ай бұрын
This is not a book to _learn_ calculus, it's to **derive** calculus with proofs.
@TheCrusaderRabbits Жыл бұрын
Waterloo is a good school.
@giovannifontanetto9604 Жыл бұрын
The questions are written like a math professor is coming out of the book and joking in your face
@meteor8076 Жыл бұрын
guys, look at the image on the Spivak's wikipedia page, he is trying to sniff his own socks :D :D
@jesusandrade1378 Жыл бұрын
That image is from 1974. And Spivak was showing his flexibility by touching the tip of his foot (tennis shoe) with his nose.
@mhas9110 Жыл бұрын
A calculus course - which solves all the problems in the book... 😁
@vinayabhat6006 Жыл бұрын
But is it good for Like the first intro to calc...
@coleyoutubechannel Жыл бұрын
I'd go with Stewart Calculus for a nice intro to calculus. This might be better suited for someone who has taken a proof writing course
@khawar0o7 Жыл бұрын
This book is not for beginners. Read Stewart's Calculus and do practically every problem from RD Sharma. Also take a look at Amit Agarwal's Play with Graphs.
@lacku2677 Жыл бұрын
God no lmao
@meteor8076 Жыл бұрын
@@coleyoutubechannel yes, this book is named "calculus", but actually it is real analysis
@vinayabhat6006 Жыл бұрын
@@khawar0o7 Ok thankyou
@mikeshivak8 ай бұрын
Neat name
@SL-lu1wv Жыл бұрын
👍🏻
@josephpuentes4160 Жыл бұрын
Hi Professor, Could you apply some aspects of decision theory to the Nord Stream destruction? That is, could one mathematically determine by inference who did it to a certain degree? (Parameters could include: value of gain/loss, timeliness, location to neighboring countries, etc.) (Not a math major, but rather a student of philosophy)
@dylanparker130 Жыл бұрын
I wonder what you had to do / say to get kicked out of a Math chat-room! Perhaps talk trash about Euler or Gauss? 😅
@TheMathSorcerer Жыл бұрын
hahahaha those chat rooms can be fairly brutal:)
Жыл бұрын
Leithold, THE bible
@710Chri Жыл бұрын
What the fuck
@ldslmikm9393 Жыл бұрын
What is ur book colection worth?🧩
@antoniomantovani3147 Жыл бұрын
Baby Rudin its the way to read and prof...maybe not so pratical as spivak
@evaisthisiaeclaire63658 ай бұрын
Could anyone explain why that question 40 is considered hard? Isn't it easily provable using L'Hospital's Rule?