Calculus II: Final exam review!

Welcome to to calculus II final exam review! In this video, we go over a standard final exam review for Calculus II. Feel free to use the timestamps to go the question you wish!

00:00 - Introduction
01:26 - Question 1 (Radius and interval of convergence)
13:24 - Question 2 (Radius and interval of convergence)
18:24 - Question 3 (Integration as a power series)
23:25 - Question 4 (Power series representation of a function)
30:12 - Question 5 (Integration as a power series + Radius of convergence)
41:56 - Question 6 (Maclaurin series)
44:11 - Question 7 (Maclaurin series to evaluate large derivatives)
54:51 - Question 8 (Alternating series estimation theorem)
58:52 - Question 9, (Taylor's inequality)
1:04:52 - Question 10 (Parametric equation with area + Concavity)
1:13:12 - Question 11 (Tangents to parametric curves)
1:15:59 - Question 12 (Area of a polar region)
1:22:40 - Question 13 (Area of a polar region by symmetry)
1:33:37 - Question 14 (parametrization of vector functions + Curvature)
1:45:25 - Question 15 (Proof based question with vector equations)
1:51:32 - Question 16 (Equation of osculating plane)
1:56:23 - Question 17 (Equation of osculating plane with alternate method)
2:06:06 - Question 18 (Reparametrizing a curve with respect to arc length)
2:11:43 - Question 19 (Arc length of a curve)
2:16:43 - Question 20 (Surface area)
2:22:35 - Question 21 (Finite volume but infinite surface area)

[Patchoulis]

It's honestly amazing how he's able to teach better than most of the profs that are paid to teach. People like you deserve way more.

[ninjacoolbeans]

thanks for all the great videos sub. I think I speak for all engineers and everyone else that had to take a math course this year that you singlehandedly made this year of online more bearable. <3

[MathforThought]

For question 12, the graph is a little misleading. The bottom curve should touch the origin. It should not touch the positive y-axis in any way. The work is fine though.

For question 14, the cross product between r'(t) and r''(t) should be <-2, 0, 2> not <2, 0, 2>. The norm is still right though.

For question 20, I wrote 1+y' instead of 1+(y')^2. The work is still fine though. I did calculate 1+(y')^2 but I wrote 1+y' by accident.

For question 5 at 41:25, there should be a factorial on the numerator. Answer is still right.

[jacobzimmel]

Hugely appreciated! Your videos have helped me through all my first year math courses

[jackfraser]

So grateful for your videos! Don't know where I would be in math without them!

[ambermyshak]

23:43 and my brain is already going with the sneaky
(i have a final in 2 days god help me)

[kglsvwd]

Thank you so much for the videos, do you have plans to make a Math 209 playlist?

[gordonho]

Thank you so much for your time and dedication this year. 😃😃

[sambradford]

Excellent Review. Hope to have you for calculus III as well!

[yosangebremeskel]

Thank you for carrying my grade for calc I and II!! It'd be awesome if you started a series for calc III TOO :)

[adamkp_]

Are you going to be covering Linear Algebra in time for the final as well? Appreciate you <3

[jasonmantri]

Why is it that we use ii at n=0 and n=1 rather than i in example 7?

[jasonmantri]

In example 14 for a and b in the cylinder equation, can they be anything????

[wadeyang]

Thanks so much for your video! I have one question with the question 1. How do you know the absolute value of (x+1) is smaller than 1? I think the question doesn't give out the range of x.

[bensonho]

for the surface area on question 20, do we not have to square the y' ? at 2:19:24

[anjjk]

this video helped so much.. thank you sub

[jasonmantri]

how is T(pi/2) is -1, 0, 1 in example i am quite lost on that.