Solving My Calc 2 Exam#2 (improper integrals, approximating integrals, & separable diff eq)

live! 0:00
Problem 1: 1:14
Problem 2: 9:25
Problem 3: 13:50
Problem 4: 20:00
Problem 5: 31:00
Problem 6: 35:29
Problem 7: 40:07
Problem 8: 51:25
Problem 9: 1:06:30
Problem 10: 1:23:16
Problem 11: 1:34:02
Problem 12: 1:40:12
Problem 13: 1:47:30
Thanks to The Math Aces for the above time stamps

Some small errors:
At 5:04, the unit should just be m^3 not m^3/min
At 1:09:20, the answer is 1/e not e

#bprplive

[themathaces]

Problem 1: 1:14
Problem 2: 9:25
Problem 3: 13:50
Problem 4: 20:00
Problem 5: 31:00
Problem 6: 35:29
Problem 7: 40:07
Problem 8: 51:25
Problem 9: 1:06:30
Problem 10: 1:23:16
Problem 11: 1:34:02
Problem 12: 1:40:12
Problem 13: 1:47:30

I was too lazy to do (a) and (b) separately but here you go. (By the way, your voice is so AMSR for me idk why)

[miquelcamprubi]

anyone feels like they would like to be friends with this guy. He seems so nice and a hell of a good teacher!

[blackpenredpen]

The video starts at 1:14
Thanks to everyone who showed up and did the math together.
I would also like to ask if any of you can comment the time stamps for this video. I will greatly appreciate it. Thank you.

[tchd]

5:07 I think it should be 0.08m^3 without /min

[atharvasharma]

live! 0:00
Problem 1: 1:14
Problem 2: 9:25
Problem 3: 13:50
Problem 4: 20:00
Problem 5: 31:00
Problem 6: 35:29
Problem 7: 40:07
Problem 8: 51:25
Problem 9: 1:06:30
Problem 10: 1:23:16
Problem 11: 1:34:02
Problem 12: 1:40:12
Problem 13: 1:47:30

[abiotic]

Calc 2 exam done at June, but still so cool... Now been studying Analytical mechanics. Anyone else from 🇮🇹?

[fpforever]

I love yout channel mainly cuz of how you can explain problems so easily. Idk anything about calculus since its exclusive to universities in my country, but I love your algebra videos. Keep it up man!

[helo]

wow, finally, I have been waiting for this for a long time

[Metalhammer]

Honestly for the first my chemist brain was like "concentrations are going to hit equilibrium. Equilibrium would mean we add the volume of all the air on earth with the air of the class room and add the total amounts of CO2 and divide or we see the 200m^3 are nothing compared to the atmosphere aka equilibrium is gonna hit at the 0, 04% whatever this percentage maybe. Volume/molar percentage or mass" And then I remembered this is maths, so I probably shouldn't think without any maths at all^^ Still I'm fairly confident that 0, 04% is the answer because, assuming we do it stepwise, the concentration will go down with every minute if we act like time flowed discretely and it can't go below the 0, 04% no diff equation needed. and because it'S a trick question we just multiply by the volume^^

[rodrigomartinho]

In the first question the unit of the answer is wrong. It's volume, not flow rate.

[JhonatanNeneh]

In my proof of calculus 2, there were no applications, only theories, tending more to Pure Mathematics. And I like this! However, it was very pleasant to see its resolution. Thank you! With love from BR

[plislegalineu]

in the differential equation (idk about 45:00) when I had (y-4)/(y+1) I did long division and got the final answer y = 10/(3e⁵ˣ + 2) - 1

[charles]

why is the solution to the first problem 80 liters per minute. Since they ask for the amount and not the rate of change then the answer should just be 80 liters

[DarkRedZane]

22:57 I didn't know about this "THE LIST"! Thank you man! Although I still got the correct answer (c.) by careful observation (or intuition), but this handy "THE LIST" would have been a big help when I was still in my Calc 2 class. I wish I saw this "THE LIST" before.

I'm still glad overall that I can answer most of the questions here correctly. ^_^

[damianbla]

01:39:30 This improper integral is convergent.
But it is convergent to which value?
To value 1? To value 1/3?
How to calculate this?

[bettkitty]

brings me back to my college days. (About four years ago i took calc 2.)

[borderjumper]

Was very surprised to see Diff eq on a calc 2 exam. Didn’t see them till it’s own course after multivariable calculus at my school

[Dalton]

The answer for for Q3 is approximately 21.5873 rounded to the nearest ten thousandth

[ami_ex]

Dear Professor Blackpenredpen, I understand that you might be onto higher academic but is it also possible if you can put out a video on WMTC/WMI/ AMC related questions for me?
Sincerely, Your subscriber student👩‍🎓 👨‍🎓

[GhostyOcean]

For 6, you didn't specify the range of f. Therefore you can assume f can get as nasty as you want, assuming it's still convergent. For (a) and (c), f could be 0. For (b), f could be negative. Since 1/x≤1 for x≥1, f(x)/x ≤ f(x), so it converges if f converges

For 9,
(a) use The Fact
(b) x²-x

For 11, since x≥2, both the numerator and denominator are always positive. If we make the numerator larger and denominator smaller and show that this larger function is also convergent, then we know that the original is convergent by comparison test. So since x² > x²-2 and x^5 < x^5 +2x^3 +6, then (x² -2)/(x^5 +2x^3 +6) < x²/x^5 = 1/x^3, which converges by p series test.