Limits and Logarithms

This calculus video tutorial explains how to evaluate certain limits at infinity using natural logarithms. It explains where the number e comes from.
Introduction to Limits: • Calculus 1 - Introduct...
How To Evaluate Limits From a Graph:
• How To Evaluate Limits...
Evaluating Limits By Factoring:
• Evaluating Limits By F...
Limits of Rational Functions :
• Limits of Rational Fun...
Limits of Radical Functions:
• How To Evaluate Limits...
Limits of Trigonometric Functions:
• Limits of Trigonometri...
___________________________________
How To Find The Limit at Infinity:
• How To Find The Limit ...
Infinite Limits + Vertical Asymptotes:
• Infinite Limits and Ve...
Limits at Infinity With Radicals:
• Limits at Infinity Wit...
Limits of Absolute Value Functions:
• Limits and Absolute Value
Limits of Composite Functions:
• How To Find The Limit ...
The Squeeze Theorem:
• Squeeze Theorem
____________________________________
Limits and Logarithms:
• Limits and Logarithms
Limits of Exponential Functions:
• Limits of Exponential ...
Piecewise Functions - Limits:
• Piecewise Functions - ...
3 Step Continuity Test:
• 3 Step Continuity Test...
Continuity and Differentiability:
• Continuity and Differe...
Limits - Test Review:
• One Sided Limits, Grap...
_____________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/ooesk2yff5KliKs Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Math & Science Videos: www.patreon.com/mathsciencetutor/collections

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[@dothemath1554]

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[@muspanisho]

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[@joseluisbenavidescepeda2244]

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[@JasonSmith-gt6oi]

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Organic chemistry

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[@roohijaiswal1403]

Very nice to see this session sir.. ! I studied many topics from Vidya Guru channel as well. I got very much same questions in my exams.

[@allmight801]

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[@heheeiibu]

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[@hussainawni1151]

You are absolutely good teacher

[@apjabdulkalamfanatm6231]

You explain really well..

[@exotickhanaarif4333]

This video clearly explains what a limit is and how do we calculate it and why do we have to simplify the function to get a limit!!

[@suvarnabiradar3753]

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[@nopegaming2029]

thank you so much for saving me so many times in calculus

[@redsharkmen]

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[@seankelly8906]

In some ways, this is "backwards" in terms of defining e and hence lnx, but it's still a neat argument, and works if you instead defined lnx to be a certain anti-derivative of 1/x. Nonetheless, you'd still have to show that lnx is itself the inverse of exponential function if you did this, and even then one might wonder why exactly that (1+1/n)^n form is there, though it is apparent when you evaluate the derivatives of log and exponential functions.

[@SS-tn6tb]

Thanks so much

[@lambsauces]

Merry Christmas!

[@davidloomis6668]

i feel smart i recognized the limit was e before he solved it

[@alienwareCL]

Great video. More general, the limit as x -> infinity of f(x) = (1 + b/x)^(cx) is e^(bc)

[@heheeiibu]

Clever 😮😮

[@LivingstonMokonen]

The best teacher ..👌👌👌👌👌👌👍👍👍👍👍

[@guliyevshahriyar]

Thank you very much teacher!

[@skimbo.2002]

thank you for this one

[@realtimechemistry3864]

very good way to get e from that limit

[@HEY_AARYON]

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I'm so glad that I get so spend over $11,000 just for a semester at college to confuse the hell out of me, and then I can come home and actually learn this stuff for free.

[@1_in_8billion]

Ahahaha

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Dang, $11,000 for one semester? That's more than the amount I pay for my school in one year!

[@anferneeee92]

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[@pramodtheekshana7038]

He is an absolutely pure genius.Thank you.

[@danielbrown1933]

Thanks

[@peterlblystone2326]

In my younger years, when I was big on math, I worked out this problem in a totally different way, by expanding the expression via the binomial theorem, simplifying each term, and taking the resulting limit of each of those simplified terms. This resulted in the series 1 + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! ... and so on -- Which just happens to come out to 2.71828..., depending on how many terms one adds. In other words, the number e. Go ahead and try it! The procedure in this video is very interesting, but it seems to assume that the value of e is already known. It's nice to be able to plug in all those huge numbers and eventually get the same result, but how would one be able to accomplish that without one of today's calculators? Anyway, I just thought I'd add my two bits!

[@cpwm17]

They already knew there was a number with special properties in the range of e before they knew with precision what the number was. This technique uses that knowledge to get an e with a higher precision.

[@sikkimhills9927]

Well..tq u lot

[@vilarseirei]

you legit saved my behind

[@womav8803]

God bless you

[@ghaidaalkhiami9164]

Bro i luv u

[@mdshahidislam7984]

why we use ln after the limit

[@raka7743]

I have a question. That's why I'm here. Please help me. My textbook writes the same equation with " n tends to 0" and still the answer is e. .but if i do with 0 it's answer 1..is my textbook wrong? Or am I doing wrong? I have exam. Please help me.

[@dijkstra4678]

Its a bit circular to use the natural log to derrive e. Is there a proof that doesn't use it?

[@cpwm17]

They already knew there was a number with special properties in the range of e before they knew with better precision what the number was. This technique uses that knowledge to get an e with a higher precision, so it's not circular.

[@saala7869]

thanksssssss

[@jameswu9715]

Awwwwwww thanks so much

[@renewd]

Why are you taking derivatives before we have learned how to take derivatives. Is your patreon playlist in better order?

[@poragbora6453]

What would be n value to get 1st or 2nd places exact decimals of Natural log.

[@milestailsprower4555]

2.71

[@rtmz_judith7542]

Limite e👏👍

[@PeachSyrup-zd7xt]

Bet he won the girls through this logarizzm knowledge

[@samiulislamdurjoy]

G 192

[@metroidman7592]

Was I wrong to assume it is just equal to 1

[@Dogface1984]

ln y = 1. then "e" both sides

[@justabunga1]

1^inifnity is not always going to approach to 1 since it’s one of the 7 indeterminate forms using l’Hopital’s rule.

[@aqeelshah5801]

Please physics

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for another outstanding video/lecture on Limits and Logarithms. Although the problem was done correctly, Mr. Organic Chemistry Tutor, you confuse me by mixing up variables/notation. Instead of just letting y equal to (1+1/x )^x and go from there, you have d/dx(ln(1+1/n)/1/n), which is an error. Please correct this error in the video.

[@rookiedraconian7852]

Not everyone is here just one day before exam like me, many ppl r studying this topic the first time so they need that he doesn't skip these little steps

[@thatomofolo452]

[@williamurbanblackiii1729]

My exam doesn't allow hopitals rule :/

[@anestismoutafidis4575]

lim n-> [1+1/inf]^inf = 1

[@IHateTheSaiyanMonkeys]

bro 1^inf is an indeterminate form......

[@mathtutor7959]

X->2 x³-8/x-2

[@rookiedraconian7852]

12?

[@Johnny-vy3kh]

I legit solved it with my eyes without allat stuff bruh 💀💀

[@aakashkarajgikar9384]

0:44 What are you doing? Are you allowed to take the natural log inside the limit like that? If so, show me a proof.

[@raminrasouli191]

When I was in undergraduate, my teacher proved this theory neither using l'hopital's rule nor the binomial theory. So I know there's a third way proving this theory. I wish I kept my notes because I can't find it on KZbin. The problem with binomial method is that you have to know the series representation of e. And the problem with the l'hopital's rule is that the function is not continuous.

[@Grim_Reaper_from_Hell]

Are you really trying to prove that e=e? Limit (1+1/n)^n is the definition of e

[@Fitnessdickinmymouth]

Infinity=y (1+1/y)^y=(1+0)^y=1^y=1 Dude it's that easy

[@IHateTheSaiyanMonkeys]

bro 1^( inf) is just an indeterminate form

[@zephyrleone1665]

What if the numerator is not 1. Wha if it is greater than 1, like 2000?

[@user-ky6jg7pd6p]

يمه وش ذا الدرس المرعب

[@avishkarandika4473]

bro please name this guy's university what the f i mean