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Converging and Diverging Sequences Using Limits - Practice Problems

The Organic Chemistry Tutor
2018 ж. 25 Нау.
1 002 308 Рет қаралды
Жүктеу

This calculus video tutorial provides a basic introduction into converging and diverging sequences using limits. It explains how to write out the first four terms of a sequence and how to determine if a sequence converges or diverges by finding the limit of a sequence. If the limit exists and it equals to some constant L as n approaches infinity, then the sequence converges. If the limit does not exist or increases or decreases without bound, that is, to positive or negative infinity - then the sequence diverges. This video contains plenty of examples and practice problems of determining if a sequence is convergent or divergent using Lhopital's rule, the squeeze theorem, and properties of logarithms. It contains example problems with trigonometric functions such as sine and cosine, natural logarithms, square root functions, factorials, and exponential functions.
Improper Integrals: • Improper Integrals - C...
Converging & Diverging Sequences:
• Converging and Divergi...
Monotonic & Bounded Sequences:
• Monotonic Sequences an...
Absolute Value Theorem - Sequences:
• Absolute Value Theorem...
Squeeze Theorem - Sequences:
• Squeeze Theorem For Se...
________________________________
Geometric Series & Sequences:
• Geometric Series and G...
Introduction to Series - Convergence:
• Convergence and Diverg...
Divergence Test For Series:
• Divergence Test For Se...
Harmonic Series:
• Harmonic Series
Telescoping Series:
• Telescoping Series
__________________________________
Integral Test For Divergence:
• Calculus 2 - Integral ...
Remainder Estimate - Integral Test:
• Remainder Estimate For...
P-Series:
• P-series
Direct Comparison Test:
• Direct Comparison Test...
Limit Comparison Test:
• Limit Comparison Test
___________________________________
Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

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  • Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzhead.info/sun/p6yyY7iQpIymeWg/bejne.html

    @TheOrganicChemistryTutor@TheOrganicChemistryTutor Жыл бұрын

  • You literally have the best Calc II tutorials. It’s great learning material for everything in the course. You have a good knack for explaining things.

    @littl3soprano@littl3soprano5 жыл бұрын

    • Which is ironic, organic chem tutor lol

      @tylerdwight215@tylerdwight2155 жыл бұрын

    • learning this in pre calc lol

      @justinwalsh6060@justinwalsh60607 ай бұрын

    • I am watching it 2hrs before exam😅

      @shivnathkachhap2404@shivnathkachhap24044 ай бұрын

    • its actually not ironic at all. ANY stem or applied stem besides undergrad general bio requires strong math @@tylerdwight215

      @mondotrombo7167@mondotrombo7167Ай бұрын

  • in 30 minutes you explained half semester course

    @nursultansulaymanov@nursultansulaymanov5 жыл бұрын

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      @theadel8591@theadel85914 жыл бұрын

    • @@theadel8591 I feel like that'll be the case for us, except I bet most of it is going to be power series

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    @mk3a@mk3a5 жыл бұрын

    • same

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  • I watched several videos explaining convergent and divergent but only this video makes me fully understand the concept. Kudos and thank you

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      @jgc9199@jgc91995 жыл бұрын

    • Yes it is cause the lim as n>infinity of ln(1+(1/n))/(1/n) is ln(1+0)/(0) which is undefined.

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    @evoxd2245@evoxd22455 жыл бұрын

  • Professor Organic Chemistry Tutor, thank you for using multiple well-known examples to explain/analyze Converging and Diverging Sequences in Calculus Two. In all Calculus textbooks, there is a whole chapter on Sequences and Series. This is an error free video/lecture on KZhead TV with the Organic Chemistry Tutor.

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    @user-wr8yg8ix6r@user-wr8yg8ix6r6 жыл бұрын

  • for anyone else scratching there head at this! plugging in inf into (1+1/n)^n = (1+1/inf)^inf = (1+0)^inf = (1)^inf = 1^inf = undefined this is why we had to solve it

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    @lampcamper6604@lampcamper66043 жыл бұрын

  • At 4:30 why do you multiply the top and bottom by 1/n? How do I recognize when to use this?

    @mynameisgrand8937@mynameisgrand8937Ай бұрын

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  • why would you add the last step at 22:15? 1/(n+2) is just 1/infinity which is zero. Absolutely no need to multiply top and bottom to get the zero in the numerator

    @benhigh1910@benhigh19103 жыл бұрын

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    @LustBug@LustBug5 ай бұрын

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    @ilyessliloch7330@ilyessliloch73302 жыл бұрын

  • for the question at 13:44 couldn't you just simplify sin(n)/n to 1? Is that an identity that can be used?

    @vestia8444@vestia84443 жыл бұрын

  • Should not we apply stolz-cesara instead of l’hospital when dealing with sequences? Please explain!

    @Blockwise2@Blockwise23 жыл бұрын

  • Will give u a good idea about convergence nd divergence. But formaly the idea of Convergence nd divergence is different.

    @mansafabrar6872@mansafabrar68722 жыл бұрын

  • why do u use l'hopital rule insted of just substitute infinity in the equation lim n-> infinity n * sin(1/n)??? and all your video are just unreal. u made life easy for us.

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  • Loved it.... thanks

    @rameshwari@rameshwari5 жыл бұрын

  • for 13:21 why can’t we use lopital rule and make it lim cos(n) = 1?

    @nabilah2510@nabilah25104 жыл бұрын

  • Great tutorial

    @parvathy4222@parvathy42222 жыл бұрын

  • you are a great help thanks

    @princecarlman7067@princecarlman70673 жыл бұрын

  • Could you not have used L'Hopital's rule for the limit as n approaches infinity of a_n = 8n/3n-5? (5:35)

    @isaackim9181@isaackim91813 жыл бұрын

  • How did we find vertical asymptote as 5/3??

    @HabibUrRahman-sr2wn@HabibUrRahman-sr2wn2 жыл бұрын

  • Thank you!

    @halleyjabbar4056@halleyjabbar4056 Жыл бұрын

  • This is really helpful , thanks though

    @anderuvivian@anderuvivian Жыл бұрын

  • I love you man :D TY

    @andrejzlatevski4290@andrejzlatevski42902 жыл бұрын

  • Wait so at 22:55 why do you multiply by 1/n instead of just evaluating the limit there??

    @spammusubi1607@spammusubi16072 жыл бұрын

  • Watching this 20 minutes before my final

    @dumoraru@dumoraru2 жыл бұрын

  • nice one. thank you

    @lima5tad598@lima5tad5985 жыл бұрын

  • Great video bro thanks it all clea

    @vedantrajpurohit8346@vedantrajpurohit83463 жыл бұрын
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