If you spot any mistakes, please comment below and I will add them to the description later. Thank you!
@edwardhuang58852 жыл бұрын
idk if anybody has spotted this already but at 7:13:23 the numerator of the final term should have been "n" not "n^2"
@tambuwalmathsclass2 жыл бұрын
GOAT
@jozhaoyuansong69372 жыл бұрын
Could you add the question 42 please? I can't solve it without using the l'hopital's rule. Thanks !!
@0123vegeta2 жыл бұрын
Not sure if mistake or I'm wrong. But question 39. Arccos(sqrt(3)/2). Isn't it +π/6 and -π/6 So D.N.E? Great video btw!
@aaaaaa-rr8xm2 жыл бұрын
I was just watching your 100 integrals video
@codyriceandothers2 жыл бұрын
everyone's impressed that you can solve 100 limits in one take, but I'm impressed how you can stand up for 7.5 hours straight
@blackpenredpen2 жыл бұрын
That’s called being a teacher. 😆
@YoavZilka2 жыл бұрын
@@blackpenredpen we stand with you teachers. Pun intended
@jeremygodoy182 жыл бұрын
nothing beats manual.
@j.m.8895 Жыл бұрын
And holds the microphone for 7+ straight hours.
@asilbek5727 Жыл бұрын
@@blackpenredpen You are literally the best teacher to learn math from. Better than all the professors I know
@nocturnalvisionmusic2 жыл бұрын
*this calculus master ain't got no limits* 😎🥳
@PovertyBench2 жыл бұрын
Nah you just gotta use L’Hopital’s rule and you’ll find the limit
@nocturnalvisionmusic2 жыл бұрын
@@PovertyBench :)
@good-luck-ugo8 ай бұрын
Yo, that's a sick comment
@nocturnalvisionmusic8 ай бұрын
@@good-luck-ugo aww yeah thank you! 🥰
@tatamata5152 жыл бұрын
Next 100 differential equations
@user-wu8yq1rb9t2 жыл бұрын
I'm agree 👍
@soumalyaghosal38542 жыл бұрын
Yeah🔥
@Nutshell_Mathematica Жыл бұрын
Agree too
@musiclofi3789 Жыл бұрын
Yeah man
@mcalkis5771 Жыл бұрын
Bruh you'll get the man killed. A differential equation can take like 10-20 minutes to solve.
@stephenbeck72222 жыл бұрын
Yes this is right in the middle of my Calc BC class. We will just watch this instead of having class (we are working on limits anyway!).
@blackpenredpen2 жыл бұрын
Your semester starts already?!
@stephenbeck72222 жыл бұрын
@@blackpenredpen high school in the south. Some places started august 1st
@blackpenredpen2 жыл бұрын
@@stephenbeck7222 that’s so early!
@integrationmaster2 жыл бұрын
@@blackpenredpen Mine's Already Started Too!
@super92962 жыл бұрын
@@blackpenredpen very early indeed.
@blackpenredpen2 жыл бұрын
Big thanks to Abby for helping me with the timestamps! [Q1 to Q10] use the graph Q1, 0:48 Q2, 7:26 Q3, 13:16 Q4, 17:29 Q5, 22:01, limits of sin(x)/x Q6, 26:46 Q7, 34:32 Q8, 38:45 Q9, 49:11 Q10,52:55, limit of tan^-1(x) [Q11 to Q20] Limits from piecewise functions Q11,57:25 Q12,1:00:31 Q13,1:04:29 Q14,1:09:11 Q15, 1:13:20 Q16, 1:16:21 Q17, 1:19:40, limit of abs(x)/x Q18, 1:23:10 Q19, 1:26:59, limit of the floor function, floor(x), aka the greatest integer function Q20, 1:32:33 [Q21 to Q35] limit as x goes to a, do not use L'Hospital's Rule Q21, 1:35:29, factor & cancel Q22, 1:38:38 Q23, 1:41:54, use the conjugate Q24, 1:45:31 Q25, 1:49:01, expand Q26, 1:53:05, just plug in Q27, 1:55:09, factor the sum of two cubes Q28, 1:58:28, polynomial long division or synthetic division Q29, 2:04:45, simplify the complex fraction Q30, 2:07:50 Q31, 1:12:34 Q32, 2:17:08 Q33, 2:22:08, multiply the lowest common denominator Q34, 2:24:57, factor x-8 as a difference of two cubes Q35, 2:28:45, use the conjugate [Q36 to Q45] limits at infinity Q36, 2:32:59 Q37, 2:34:36 Q38, 2:35:58 Q39, 2:41:49 Q40, 2:43:23 Q41, 2:45:08 Q42, I accidentally skipped this... Q43, 2:47:22 Q44, 2:50:38 Q45, 2:55:04 [Q46 to Q55] definition of derivative in terms of the limit Q46, 3:02:36 Q47, 3:08:48 Q48, 3:13:08 Q49, 3:16:32 Q50, 3:19:44 Q51, 3:25:42 Q52, 3:32:40 Q53, 3:35:36 Q54, 3:41:51 Q55, 3:49:56 [Q56 to Q70] L'Hospital's Rule Q56, 3:56:06 Q57, 4:05:28 Q58, 4:13:40 Q59, 4:16:25 Q60, 4:20:40 Q61, 4:22:49 Q62, 4:25:25 Q63, 4:28:33 Q64, 4:34:05 Q65, 4:37:22 Q66, 4:40:02 Q67, 4:41:24 Q68, 4:43:56 Q69, 4:49:41 Q70, 4:55:20 [Q71 to Q80] my limit secret weaspons Q71, 5:02:21 Q72, 5:04:54 Q73, 5:06:55 Q74, 5:08:09 Q75, 5:09:03 Q76, 5:14:34 Q77, 5:15:35 Q78, 5:17:26 Q79, 5:22:15 Q80, 5:24:12 [Q81 to Q90] the epsilon-delta definition of a limit Q81, 5:26:27 Q82, 5:35:55 Q83, 5:41:03 Q84, 5:45:05 Q85, 5:51:54 Q86, 5:56:46 Q87, 6:05:02 Q88, 6:10:37 Q89, 6:18:45 Q90, 6:24:49 [Q91 to Q100] limit as integrals (Riemann Sum) Q91, 6:32:37 Q92, 6:44:34 Q93, 6:52:59 Q94, 6:57:20 Q95, 7:04:06 Q96, 7:08:39 Q97, 7:10:09 Q98, 7:11:25 Q99, 7:13:30 Q100,7:19:00
@atomspalter20902 жыл бұрын
thanks for the timestamps
@IlIlllIlll2 жыл бұрын
Hello BPRP
@octopuskeng2 жыл бұрын
I am so excited to watch this video!
@atomspalter20902 жыл бұрын
@@octopuskeng same
@integrationmaster2 жыл бұрын
Can't Wait :))
@ngrm2 жыл бұрын
You're my hero man. As an aspiring math educator, I see this level of dedication as a force of nature.
@ralphhebgen7067 Жыл бұрын
Wow. I am seriously impressed. 7.5h standing up straight, maintaining mental focus, and explaining things lucidly. The only thing I have ever done for that long without a break is sleeping… 🤘👍
@showtimemaster1824 Жыл бұрын
He is a math menace! Someone give this man a raise!
@tambuwalmathsclass2 жыл бұрын
You are doing absolutely an incredible work, I'm just Imagining how possible I can talk for 7 hours 😲 May God bless you more 💪
@blackpenredpen2 жыл бұрын
Thank you so much 😀
@du42bz2 жыл бұрын
Can you prove the existence of your imaginary god?
@Francesco-ib7dx Жыл бұрын
4:54:45 we can factorise the same way we did with the limit of x approaching 0+ and we get: lim x--> infinity (24x^7)/(64x^7 - 24x^4) = lim x--> infinity 24/(64 - 24/x^3); substitute infinity and we get 24/64 = 3/8 5:16:35 we can rewrite as e^ (lim x-->infinity(x^2ln(1-1/x))) We can use l'hospital rule for the limit if we rewrite it as lim x -->infinity (ln(1-1/x)/1/x^2) then we get lim x -- > infinity (1/x^2 -x)/(-2/x^3) adjust the fraction and simpliy: lim x --> infinity (x^2/(-2x+2)) this is just negative infinity so we have e^negative infinity which is 0 by the way keep doing this its amazing and i don't know how you can stay focused for 7 and a half hours straight.
@chennebicken3722 жыл бұрын
Love, how you make so much maths accessible to everybody. This is so valueable for „normal“ people but also so practical for people who study mathematics. ❤️❤️❤️
@yashyadav6022 жыл бұрын
broo like I am not even a calc student yet but I fricking love this vids... I solve all these integrals with you... Thanks for being so awesome
@blackpenredpen2 жыл бұрын
Thanks. I am happy to hear it 😃
@Cm-zc2zx2 жыл бұрын
Kis class me ho bro?
@colleen94932 жыл бұрын
@Yash Yadav that was me a few years ago, you’ll love calculus.
@mathmancalc77532 жыл бұрын
You're like a paradox. You're skills are both limitless and not "limit"- less
@blackpenredpen2 жыл бұрын
hahaha thanks
@gvacv8 ай бұрын
3:16:10 still watching, indeed!!! I really really appreciate your effort, professor! It's a little bit sad when you say your arm hurt or that you're sweating, but then it gives me strength to not give up too!
@blackpenredpen8 ай бұрын
Thanks! I run marathons, so I am determined in the things I do. I am happy that this video motivated you as well!!
@Lil_electrician2 жыл бұрын
I watched the 100 integrals and also the 100 series, they are very helpful for getting the main idea and getting practice for them thank you
@blackpenredpen2 жыл бұрын
Great to hear! Thanks.
@mathesaurus36212 жыл бұрын
These videos are genuinely helpful and great for people who are doing calculus 1 and 2, thank you for making these videos and making our lives much simpler
@Johnny-tw5pr2 жыл бұрын
Q60: write x as e^lnx then you have e^(lnx+1/x) which from the previous limit we know tends to infinity so e^inf = inf
@pawloszeyede5787 Жыл бұрын
Man is a legend! Thanks so much. I nailed my Calc Mid term because of your videos. God bless.
@blackpenredpen Жыл бұрын
Glad to hear! thank you. Good work on your end, too! : )
@tim1753 Жыл бұрын
"doing limits is like a box of chocolate, you never know what you're gonna get" 4:19:56 Love this one
@grindpalm2 жыл бұрын
"Limits are like a box of chocolates... you never know what you'll get" ❤
@blackpenredpen2 жыл бұрын
hahaha!
@saturn2334 Жыл бұрын
but you know its gonna be chocolate , if its a box of chocolate
@trishaamps2 жыл бұрын
I'm in my 4th year of engineering and I needed a refresher on this. Thank you so much
@pianodan16082 жыл бұрын
It’s amazing that he is so determined to do math! Your dedication and perseverance inspire others!
@najibqunoo72322 жыл бұрын
the missing limit is 3 (2^x + 3^x)^(1/x) = ((3^x*(1+(2/3)^x))^(1/x) = (3^x)^(1/x) * (1+(2/3)^x)^(1/x) = 3(1+(2/3)^x)^(1/x) plugging infinity for x in this term we would notice that it would approach: 3((1+0)^0) = 3 we could also rewrite everything here in another form like: 2^x(1+(3/2)^x)^1/x if we got asked about the limit for x approaching negative infinity, we use the same procedure and notice 2((1+0)^0) = 2
@najibqunoo72322 жыл бұрын
it would be nice if you recovered this in a later video
@blackpenredpen2 жыл бұрын
@@najibqunoo7232 Yea I plan to do so.
@mistcipriano396 Жыл бұрын
Thank you, up
@gruesomedevil5062 Жыл бұрын
i like how you dont solve questions for just the sake of it and actually teach everything i am doing this series as practice questions and learn a few things every now and then even though i have done this chapter 3 times from youtube
@blackpenredpen Жыл бұрын
Glad to hear. Thank you!
@gruesomedevil5062 Жыл бұрын
@@blackpenredpen 🖤❤
@johndouglasclark1309 Жыл бұрын
Still watching, Q48, you truly are so motivating, your dedication is motivating and makes me not want to stop working hard!💪
@blackpenredpen Жыл бұрын
Glad to hear!!! Keep up ur good work too!
@505steel2 жыл бұрын
I just made it through Advanced Calculus/Real Analysis this summer because of this channel! Thank you!
@blackpenredpen2 жыл бұрын
Great to hear!
@farouk64376 ай бұрын
I didn't study the last two weeks for personal reasons, then the last day i spent the 7h30 hours on this video (with pause for doing exercises after he show the answer is gonna be a solid 15h). While chewing a watermelon chewin gum. The day of the exam i chewed the same watermelon chewin gum and i was able to recall the exercises from this video and the answers and explanation! I got a solid 94% final exam. Hope this advice can help some of you guys!
@killer-bee0Ай бұрын
OMG that's really insane that you complete like 10 videos of 100 math problems🥶
@God-ld6ll2 жыл бұрын
"your limits dont even exist"
@rayanselmani4802 жыл бұрын
What do you mean about that
@Mozalthiric2 жыл бұрын
@@rayanselmani480 has to do with limits and calculus
@rayanselmani4802 жыл бұрын
@@Mozalthiric ^_^
@AbhishekMishra-lt2fi7 ай бұрын
sir you explain better than my class 11th science maths teacher she just a noob maths and God knows how she became teacher.
@gustavosouza5600 Жыл бұрын
i am just impressed that someone could spend 7h just doing limits. i'll definitly watch it fully.
@blackpenredpen Жыл бұрын
Thanks!
@gustavosouza5600 Жыл бұрын
@@blackpenredpen i'm really thankfull for your content, really. I'm from Brazil and here this kind of content is not commun and eazy to found in that level os quality. you're just amazing!
@cymbalization94432 жыл бұрын
Watched your video since the start of my A-level course last year, from not having a clue, to knowing more and understanding more in the different perspective. Love your vids, it’s really helpful in giving me ideas to solve my math problems creatively.
@thygovanengeland8758 Жыл бұрын
His enthusiasm makes me want to do all his 100 series (which I am). Thank you for your dedication!
@adamlopez2339 Жыл бұрын
I've seen the whole video, absolutely amazing. Appreciate the effort on your videos, keep going
@blackpenredpen Жыл бұрын
Thanks a ton!
@elhaunterelegante545 Жыл бұрын
For those wondering about the limit of Q42, it is 3. I recommend to make it similar to an 1^infinite indetermination
@mistcipriano396 Жыл бұрын
can you explain? idk how to make this without lhopital or special limits. I know it's 3 because i saw on geogebra but idk why
@ScampSkin2 ай бұрын
This is one of my favourite series on YT. I hope you will be doing more episodes although this is exhausting and time-consuming. You are really helping people and not only those who are students but those who try to self-educate and change their lives. Much respect my man
@user-tt2po5wg7n7 ай бұрын
He is a math menace! Someone give this man a raise!. this calculus master ain't got no limits .
@ESOMNOFUONLINEMATH2 жыл бұрын
My role model. I do maths here, but I always salute you
@armilo52 жыл бұрын
Thank you so much for making these types of videos! The 100 integrals and 100 series videos were super helpful when preparing for my Calc exam ❤️
@blackpenredpen2 жыл бұрын
Glad it was helpful!
@StaticBlaster Жыл бұрын
in ONE TAKE! holy jesus. This guy's channel should be called TheMathBeast, TheMathGod, or TheMathMaster
@AeroStuffFPV8 ай бұрын
Imagine forgetting to press record
@pro.x44111 күн бұрын
😂
@redweg475 ай бұрын
04:54:54 the limit when then equation goes to infinity is 24/64=3/8. You are so awesome!
@mustaphamomo9315 Жыл бұрын
a genius ,you need all the support.
@Peter_19868 ай бұрын
Man, the epsilon-delta examples were explained a hell of a lot better in this video, compared to the chaotic mess from my math teacher.
@bijanyeganeh8181 Жыл бұрын
I love your T-shirt and the fact that you are holding the mic for this long, love you man you are doing a great job, truly what a real teacher does
@vickyvazzm352210 ай бұрын
I just want to thank you for your content, you literaly made me love calculus
@blackpenredpen10 ай бұрын
Happy to hear that!
@YoavZilka2 жыл бұрын
Love these kind of videos. Can’t imagine how much effort you put in them
@piashasan5136 Жыл бұрын
From Bangladesh 🇧🇩.... I am surprised what a patience in you... I watched fully.,🥰
@sadnanjuhib8 ай бұрын
Which grade are you in?
@studiouskislay9 ай бұрын
4:54:43 the answer is 3/8 5:16:36 the answer is 0 Thank you for everything sir ❤
@kamoliddineshkobilov89268 ай бұрын
I got + inf for the second one
@pooqy2 жыл бұрын
2:48:48 That should be x-1 in the square root ♥ If I spot any more mistakes I will be sure to add more as I watch all these 7 hours of footage
@blackpenredpen2 жыл бұрын
Thank you!!
@bhavyapal2 жыл бұрын
Glad you did this video about 100 limits it will help me in preparing for my upcoming exam.
@Happy_Abe2 жыл бұрын
@7:00:45 the functions is sin(x) from 0 to pi
@takeoverurmemes2 жыл бұрын
the captions may not be 100% accurate, but someone really went and put captions out for 7 and a half hours worth of video that's actually insane, bless whoever took the time to do that
@tumelosibiya594 Жыл бұрын
Thank you so much, I am doing engineering and this calculus has been beating me up, writing an exam on Friday and I feel ready because of you. I've recommended you to many of my classmates since they were also struggling. Thank you.
@Splixly Жыл бұрын
you are the coolest guy i have ever seen on youtube
@djezio258 Жыл бұрын
This is the video I was looking for! I might not watch it entirety by once, but fast-forward to the limits I have most doubts in solving them, then I'll come back everytime I need to refresh my mind about them. Math is power
@konoveldorada59902 жыл бұрын
Hey, I have a fun question for you :) In Ellipse, (x/a)^2 + (y/b) ^2 = 1. *Then find out (a/x) ^2 + (b/y)^2*
@pratyushmishra46782 жыл бұрын
If I am correct then it must be (2cosec2A) ^2 with A as the parameter with ref to auxiliary circle.
@satestactmathtutor6570 Жыл бұрын
you are an absolute genius brother plz keep making videos for all of us.I am a machine learning engineer and your videos helped me so much through out my career
@tim1753 Жыл бұрын
I finally finished this video, and I learned a lot. Thank you so much, you continue to make me love maths even more, as always
@ayonbarua24 Жыл бұрын
I can't be more thankful to you Steve. So far you have been the carrier for me in my whole calculus study. I have learnt infinite amount of techniques through your 100 everything series and I hope that you will carry on this series. I hope to meet you once if I ever get a chance to do so. Love from Bangladesh.
@user-pn6es6ju9v Жыл бұрын
Man you're amazing, 😮 you stand 7hrs straight, holding mike and speaking for 7 hrs? I couldn't even able to finish watching your video
@user-tp4mj8rl2f8 ай бұрын
جزاك الله خيرا ❤
@AltinoSantos2 жыл бұрын
Congratulations! Yes, you have no limits. You deserve 2 million subscribers! 👏👏👏
@fernandocupil.6463 Жыл бұрын
Plsss dont quit making videos like this. You are my heroe. Eres mi ejemplo a seguir
@Morphysince942 жыл бұрын
the legendary series is BACK!!!! ❤❤❤
@aysenuraydn91072 жыл бұрын
i am from turkey, thank you so much this video. my english is bad but I understand you, thank you math language!!!!🤩
@rshawty2 жыл бұрын
the title’s funny coz as a french person I read “100 limits” like “cent” (=“hundred” in french) + limits and it sounds exactly like “sans limite” which means “no limit”, lmao voilà jambon beurre baguette
@DarkInTheNight2 жыл бұрын
Ham butter baguette?
@rshawty2 жыл бұрын
@@DarkInTheNight yea
@kangaiman5398 Жыл бұрын
This video makes my daily 2-hours-on-my-way-to-school so fruitful as a newbie to calculus. Thank you.
@goodforyou95962 жыл бұрын
The limit of his hard work is the limiting value of the logos on his t-shirt❤️
@Joshinthetronk Жыл бұрын
I have just started taking calculus and I absolutely find it fascinating!!!! Thank you for this wonderful video
@theshadow92382 жыл бұрын
As Calc BC approaches Semester 2, my homework approaches infinity
@yohannesaschenaki54062 жыл бұрын
Bro just calculus master...really you always inspire me to do more calculus love from 🇪🇹🇪🇹
@mathsphilus Жыл бұрын
Dude you went so far!! this is the true love of teaching, And also you r not boring I can watch this to the end. thank you so much.
@jaykay2218 Жыл бұрын
Bro, you’re honestly an inspiration
@blackpenredpen Жыл бұрын
thanks!
@Livio_05 Жыл бұрын
5:16:30 Well i guess you could say it's equal to (1-(1/x))^x.x, so a is -1 and b equals x. If you work this out with the formula, you'll get e^-x, but x goes to infinty, so you'll end up with 0
@thex3001Ай бұрын
I watched all of it including 101 thank you so much you started from easy to hard especially thankful for the last part finally understood the connection between the Rieman sum, limit and Integral! and my analysis exam is next month!
@DmitriNesterov7 ай бұрын
Маньяк ты! Глубочайший респект ❤
@CreativeDimension2 жыл бұрын
The answer to the question at 5:16:38 should be infinity as the expression will boil down to "lim x->infinity e^x", putting in the value results as infinity.
@josepina9399 Жыл бұрын
For those wondering, the answer in the extra question at 4:54:50 is 3/8. I used L'Hospital's Rule 3 times
@alessandrofaranca1309 Жыл бұрын
@@josepina9399 i don't think it is the answer, instead it might be 0 from 1/e^x
@PetrilloProduction Жыл бұрын
After first L'Hopital you get both x^8 so you can only watch about the coef. and get 3/8 :)
@roshinis9986 Жыл бұрын
to use the L'Hospital's rule, you must first bring it to u/v form. I don't think you did that.
@joshhh___ Жыл бұрын
@@josepina9399 After taking the natural log of both sides, you should get ln(L) = lim x->inf (x^2)ln(1-1/x). The right hand side can be written as ln(1-1/x)/(x^-2), which allows us to use L’Hopital’s Rule.
@communist_amoeba3923 Жыл бұрын
WHAT! just multiply divide by (x-1) and we know x^n-a^n=na^n-1 obviously its 3/8
@prapti2385 Жыл бұрын
My personal timestamps:- graphs:- Q)12 Q)13 Q)17 Q)28 Method of synthetic division 3:16:00 Sir I am still watching, thank you so much for making this video. I understand that it's really difficult to teach standing for 7hrs straight and that too to a camera. Hats off to you!❤️🤗
@shivensaini36432 жыл бұрын
Sir, I really thank you for The list you showed us at around 5:05:00. Very helpful, solving limits questions is very fast now.
@blackpenredpen2 жыл бұрын
You are welcome
@jeanalex76982 жыл бұрын
Who made the subtitles is definitely a king
@lostinthebluecity Жыл бұрын
I did that ..!! I can't believe it myself.. I solved it from 1 to 100... thanks bro.. 🤘
@VincentGoossens-tu8pd Жыл бұрын
amazing teacher, lots of respect you make people enjoy math. incredible work thank you, you really helped me!
@astrogds28167 ай бұрын
Thank you for these long videos, it really helps mastering the concept !
@anayagrawal65502 жыл бұрын
7:00:49 The function is sin(x)
@icicle21802 жыл бұрын
4:22:35 "Sometimes infinity can win too!"
@DokterrDanger2 жыл бұрын
You can try 100 definite triple integrals next I believe you can do it
@John010 Жыл бұрын
i know this might be rude, but this being the background "music" for doing homework is the best
@Anonymous314162 жыл бұрын
A Great thanks to you Sir 😊, to give us an ample amount of limit questions ( both graphically and algebraically)
@edit3907 Жыл бұрын
We want 100 integration part 3 please ❤️☺️
@joaovictorsouzadeandrade97132 жыл бұрын
Now my Friday is gonna be interesting
@andrewkachedwa3164 Жыл бұрын
You are much appreciated because u improved my performance in mathematics 🙏🙏
@andrewstephengames12602 жыл бұрын
I got 3/8 for 4:54:43 Edit: Also I got e^(-x) for 5:16:35
@Happy_Abe2 жыл бұрын
@5:16:40 0
@bsl33996 ай бұрын
It's a best way to learn mathematics, I wasted months to learn but only 6-7 hours is enough to solve math ,
@warsw5262 Жыл бұрын
man's just math's own GOAT
@amir_xtz92211 ай бұрын
you are a life-saver❤. Watched this from Q1 to Q101 entirely.
@mathsis99632 жыл бұрын
i have my maths exam after 10 days ...watching this make me fire and now i am ready to burn out solving maths
@QuranReact1 Жыл бұрын
For Q60, here is another way to do it : we can rewrite x*e^(1/x) as e^((x*ln(x)+1)/x). And previously in Q59 we already calculated lim as x goes to 0+ of ((x*ln(x)+1)/x), which is +infinity. So we can deduce that the limit as x goes to 0+ of x*e^(1/x) is equal to +infinity.