Comparison Tests | MIT 18.01SC Single Variable Calculus, Fall 2010

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13 жыл бұрын

Comparison Tests
Instructor: Joel Lewis
View the complete course: ocw.mit.edu/18-01SCF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
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Пікірлер: 51

@StevenCarell 11 жыл бұрын

Thanks for volunteering your time for this! These are the tests that I have the most problems with... probably because they require thought rather than a strict process :)

@AlpNewYork 9 жыл бұрын

Amazing explanation thank you very much . I feel so lucky to belong to this generation , I can go on KZfaq and watch lectures from a world class university .

@Beatmastapat09 9 жыл бұрын

Awesome explanation of the limit comparison test thanks!

@Joeofiowa 13 жыл бұрын

fantastic presentation. perfectly paced, well articulated, and entertaining.

@tsi4ya 9 жыл бұрын

Very well explained. Thank you for the last problem, the explanation or rather the logic behind it was very different in comparison to preforming comparison test or direct comparison.

@HariKrishnan-bi6zt 8 жыл бұрын

thank you for the class.

@joydeepburman5269 6 жыл бұрын

Very well explained

@imegatrone 12 жыл бұрын

I Really Like The Video From Your Comparison Tests

@chrishanni2779 11 жыл бұрын

This is great; thank you!

@azngaiaboi 13 жыл бұрын

This guy just taught what took my PSU instructor a whole lecture to attempt to teach. He also teaches it incredibly better also.

@wellitstrue102 13 жыл бұрын

this dude rocks!

@charlesabernathy9064 4 жыл бұрын

Thanks on summations.

@thenanc100 11 жыл бұрын

you just helped me a ton :D

@bobkameron 3 жыл бұрын

Good video and explanation

@michalchik 13 жыл бұрын

Thanks, well paced, well explained, just a bit of nervousness to overcome.

@Kalistane 12 жыл бұрын

How do we know when to use this test or other tests like the ratio test or integral test? Someone help me please. :)

@georgesadler7830 2 жыл бұрын

There is a chapter in Calculus II on Infinite Series. There are ten different test for convergence in Calculus. Each Calculus student should be very familiar with each test for convergence. Professor Lewis demonstrates how to apply these test for convergence.

@lightsoff97 9 жыл бұрын

For three first example, when you allowed us to work them out ourselves, I used the nth term test, I also thought of using the direct comparison test. Should I not? Should I only use the limit comparison test?

@khonhlo1476 12 жыл бұрын

because of the p series test where 3/2 is p > 1 which converges

@consumer338 10 жыл бұрын

Wow the last one took me quite some time to figure out.. would never have thought of that method. Thank you :)

@JymeBale 10 жыл бұрын

Always try to think out side the box on everything and you may get the method, some never do others see it as they read it, it is not a big deal at all.

@pianoforte17xx48 3 жыл бұрын

I solved it in a completely different way which I thought was much easier. ln(n)

@albinsopaj 4 жыл бұрын

I think in the beginning he wanted to say: The sequence of the series, instead of the function of the series. It its true that a sequence is a special type of function, whose domain is the set of all Natural Number N, but usually people associate series with sequences not with functions.

@capaverde3340 12 жыл бұрын

how do you know that the sum of 1/n^(3/2) converges?

@YorangeJuice 2 жыл бұрын

this video is a W

@waltvanamstel6807 9 жыл бұрын

Just a minor detail I'd like to highlight. in the 1st example is shown that the sum from 1 to infinity is convergent. Not zero directly. We can say that this sum he showed converges to L. So to be specific the original sum would converge to 2+L.

@WowPlusWow 5 жыл бұрын

I love how this is from MIT but he does the easiest examples.

@CJ2345ish 10 жыл бұрын

I don't necessarily understand for problem c how you came to the conclusion that ln(n)/(n^p) always approaches zero as n goes to infinity assuming p>0.

@alexeiacevedo6367 10 жыл бұрын

This is not a proof. Just as a recap, remember he is not talking about the series, but only the function ln(x)/x^p. So we can go ahead and test two smart "p" values. Consider p=4, now look at the graph of y = ln(x)/x^4 and you will see that it seems to approach zero. Prove it is decreasing by taking the derivative and then evaluate the derivative at a smart number such as x = 100, you should get a negative value, which means it is indeed decreasing, and logically getting closer to zero. Now test other "p" value such as 1/2. Hope I helped!! Btw be carefull with the smart number "x" because you can see that these graphs have a relative maximum.

@aashsyed1277 3 жыл бұрын

0:26 GOLDEN!!!!!!!!!

@egor.okhterov 8 жыл бұрын

What is the video, where they showed the limit of ln(x)/x^p = 0 (for any p>0)?

@holysong2099 4 жыл бұрын

It's obvious like he explained that lnx makes very slow progress with n but in the denominator positive powers of n, they get very large as compared to the numerator so the ratio approaches to zero.

@egor.okhterov 4 жыл бұрын

@@holysong2099 yeah, it's obvious when p >= 1, but it's not obvious for p > 0 & p < 1

@holysong2099 4 жыл бұрын

@@egor.okhterov hmm that's right, really it's not obvious between 0 & 1.

@egor.okhterov 4 жыл бұрын

@Bob Smith It's not true. lim(x/2x) is not zero, despite denominator being always bigger than numerator.

@MrCuleito 11 жыл бұрын

Is inconclusive when you use the ratio test, not the limit comparision test. In the ratio test you take the limit of abs(an+1/an), and if the result is one the test is inconclusive in fact.

@Nitens90 4 жыл бұрын

there are some passages that are a bit clunky especially in the third integral. not recommended

@aashsyed1277 3 жыл бұрын

ACTUALLY THE LAST SERIES DIVERGES BUT VERY VERY VERY VERY VERY VERY VERY VERY SLOWLY. EDIT: THE LAST SERIES IS BIGGER THAN (PI^2)/6 BECAUSE THE LAST SERIES IS BIGGER THAN SUM FROM N=1 TO INFINITY OF 1/N^2