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.

How To Evaluate Limits From a Graph:

Evaluating Limits By Factoring:

Limits of Rational Functions :

Limits of Radical Functions:

Limits of Trigonometric Functions:

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How To Find The Limit at Infinity:

Infinite Limits + Vertical Asymptotes:

Limits at Infinity With Radicals:

Limits of Absolute Value Functions:

Limits of Composite Functions:

The Squeeze Theorem:

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Limits and Logarithms:

Limits of Exponential Functions:

Piecewise Functions - Limits:

3 Step Continuity Test:

Continuity and Differentiability:

Limits - Test Review:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

Limits - Free Formula Sheet:

[AnythingGhana]

❤️😅” woww what just happened” that part got me

[dothemath]

Thank you for always making high quality content!

[muspanisho]

The best channel to ever come out of Youtube 💯

[JasonSmith-gtoi]

What degree did you graduate with? You inspire me so much with how much you know about multiple subjects.

[exotickhanaarif]

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!!

[joseluisbenavidescepeda]

Thank you for sharing your knowledge with the rest of the mortals, I am a faithful follower of your channel, greetings from southern Colombia.
Would you be kind enough to upload a video on solving equations with matrices please.

[redsharkmen]

please make a series of videos on enzymes, hormones, neuropeptides, neurotransmitters, and gasotransmitters.🙂

[Alexnt]

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

[nopegaming]

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

[suvarnabiradar]

sir you are my best teacher in my life .

[anferneeee]

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.

[peterlblystone]

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!

[pramodtheekshana]

He is an absolutely pure genius.Thank you.

[apjabdulkalamfanatm]

Why don't you create your own app just like 'Khan academy' did
And put all your videos there (categorized)

[heheeiibu]

You're great! Brilliant, I hope I get parts of your knowledge someday

[seankelly]

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.

[realtimechemistry]

very good way to get e from that limit

[davidloomis]

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

[allmight]

more videos like this you just make math fun and easy to understand

[roohijaiswal]

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.