Estimating Sums Using the Integral Test and Comparison Test

Рет қаралды 60,273

Күн бұрын

Пікірлер: 35

@choo1030 4 жыл бұрын

integral test, root test, alternating series test were the most difficult part for me in Calculus II. Professor didn't bother explaining these test drawing on the board. After watching this, I now have much clear and better understanding.

@mrbanana6464 8 ай бұрын

The proofs are fairly easy once you sit down and properly read them through. Even if you don't follow the proofs, it's easy to apply these tests without actually knowing what they mean. It's literally just a checklist for convergence/divergence.

@Velnio_Išpera 29 күн бұрын

Integral test: 1. Ensure f(x) is positive, continuous and decreasing. 2. Look for convergence: if limx→∞ f(x)=0 (not always), then: 2. Compute improper integral of that function to find area under the curve or Sum.

@MeditacionesAlma 6 жыл бұрын

Thank you for your time and your excellent way to teach👍🏻

@obsatamasgen656 10 ай бұрын

thank you very much from my heart i learned much and my skills doubled from your tutorial

@irvirv8243 4 жыл бұрын

Teacher: -you have 24h to prepare for this topic. Me watching Dave: nah 10m is plenty of time for learning this. P.S. Another awesome video.

@bonniem1865 2 ай бұрын

thanks ppokie. still struggling a bit with ntegral test but i'll get the hang of it.

@clemja28 6 жыл бұрын

Thanks for all your work. You're a Jedi sir

@noahgsolomon Жыл бұрын

he knows a lot about all kinds of stuff

@99BeastMaker 3 жыл бұрын

Please come teach at my university...they make these things seem so abstract while they are in fact very intuitive

@asishsarkar81 6 жыл бұрын

Your explanation is really helpful

@jamesrobertson9149 6 жыл бұрын

brilliant. as usual.

@scitalks8286 2 жыл бұрын

Thank you for the awesome explanation, professor!!

@Kiky_MedPhysicist 4 ай бұрын

Thank you sir for your dedication! 🙏

@SailorJenova 6 жыл бұрын

lol, wish this was up when I was in Calculus I ! XD Oh well, still need the refresher anyways. ;) Understanding it, and not forgetting it is always important.

@shekelboi 7 күн бұрын

At first I didn't get why the first term is left out but now I see that 1/x^2 would be impossible to evaluate at the value of 0, so that's why it's left out.

@Code65115 6 жыл бұрын

Sir,as u showed that 1/(x^2) is covergent then even 1/x should also be convergent but it is diverging. Sir please tell how❓

@ProfessorDaveExplains 6 жыл бұрын

check out my tutorial on improper integrals and it will make more sense!

@carultch 3 жыл бұрын

1/x does not pass the integral test. The integral of this function also diverges, since the integral is ln(x) + C, instead of being a power function of x. This leads to the paradox of Gabriel's Horn, where a body of revolution from y=1/x from x=1 to infinity defines the shape of a horn with a finite volume, and an infinite surface area.

@CuteLoveNikky 5 жыл бұрын

Thank sir for this explanation.......

@Attalla-t9b 7 ай бұрын

Nice explanation!

@unusualfrog779 3 жыл бұрын

Epic Win Uncle Dave

@ian.ambrose 2 жыл бұрын

He's my Papa

@wayamraxama Жыл бұрын

Check at video time around 3 Minute. Limit is 2, infinity not 1 , infinity. Please correct it.

@josephsennello9773 Жыл бұрын

thank you calc jesus

@ram79la Жыл бұрын

You're amazing!!

@RF-fi2pt 3 жыл бұрын

Why the divergent harmonic series cannot proof Zeno Paradox of movement? Why is proved with the series of 1/2^n and not with that of 1/n if both sequences tends to 0 ? Ok series 1/2^n is convergent and our harmonic divergent, but if Zeno asked for 1/2, 1/3 ,1/4, 1/5 ,...,1/n to the destination, this divergent is one case Against the other convergent used to proof of movement. Is not a "math cheat" choose one sequence convenient to the proof without explain why others are not valid AGAINST that choosen? If the answer is only :"divergent is infinite sum" this gives reason to Zeno, as he have one valid infinite sum against that convergent proof. Who wins? I think have math answer to this, but post my initial fair though. PS: i see in the convergent as in each step summing 1/2^n to the acquired also remains 1/2^n to destination, as in the harmonic summing 1/n to the acquired remains (1-1/n) to destination.