L'hospital Rule: limit of x^p*ln(x)

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Limit and indeterminate form

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Great! I've watched so many of your videos that now i speak to myself in YOUR ACCENT while i do calculus. I dont even know mandarin!!

AdityakrishnaMr
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I wish that someday i could express my ideas in math as clearly as you do.
Its hard but you make it look really easy

TheNachoesuncapo
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"I can use the blue pen to cancel this x and 1"
The Blue Pen rule

galgrunfeld
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Great video! Also thanks for bringing back the "yay!" it's awesome and iconic to your channel!

RutvikPhatak
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You know, BPRP, a few years ago I really just stumbled upon this proof, and so I made up a question based on it -
What do you get if you integrate ln(x)dx, n times, calling the constants of integration each time c1, c2 etc. Then, you take the limit of that expression as x appraoches 0. It's surprisingly easy and neat for a question about integrating infinitely many times! :D

MrQwefty
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The ln could be brought down without much problem. A bit simpler even.
lnx = 1/lnx^(-1) = -1/lnx. and when you derive the bottom you get a -x overall.
d(-x^p)/d(lnx) = -px^p-1 · x = -px^p

CloudSkywalker
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Gerçekten çok faydalı videoların var. Özellikle integral videolarına bayıldım. Türkiye'den selamlar.

esra
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Show your work regarding:
lim x->0 (0^x) as well.
I liked this one.

purushotamgarg
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The auto-captions said la happy toss rule, and it was pretty good we could throw away the indeterminate form

VaradMahashabde
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I know that l might be wrong but it will be creative to do a inverse lhospital's rule.that is to say we can integrate the numerator[x^p.ln(x)] and denominator [1] from 0 to x
which will be...
L= or,
L=L/(p+1)-lim[x^p/(p+1)^2] or, pL/(p+1)=0 or, L=0

debrajbanerjee
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i did it exactly the same way when i watch the previous video! :)

maimple
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This identity is useful while putting limits in definite integration.😀😀

alankritanand
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Great video like always!! But why no board?? Are you on vacation?

willful
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Heyyo BPRP, I was just wondering, how are you soo good at Math? Like calculus and other stuff that you've presented on your Youtube Channel.. Like, you could find an elegant way to solve problems and give a nice explanation on how you do it.. Is it just me that I lack of practice? Or is it just you're that type of person that does math very well?

HVH_
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#blackpenredpenbluepen Great videos! I've been watching them for a while now, I really like your channel.

yamiddiaz
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How do you keep your phone in position to record? Sorry for the math unrelated question

blankblank
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Some math videos would be better in this format than the whiteboard, maybe this could be a not-rare thing.

MrRyanroberson
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L'Hôpital makes quotients easier.
#¡YAY!

WhiteDotX
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blackpenredpen i wanted to know whether there is any algorithm or some method to tell whether a particular functions graph forms a closed loops 🙁

quickfox
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Any idea what happened to that deleted upload yesterday or the day before?

Kuratius