Just like every week over the past few months, I had quite a slow start to this week but am happy to say that I pulled it back over the weekend and (I think) I studied for at least five hours. 💪🏼 I ended up finishing off the Course Challenge (which I’m SUPER happy about) but got my ass kicked, only getting 20/30 questions correct (which I’m much less happy about). I’m definitely disappointed at how poorly I did on the test, but there were a few bright spots from his week which somewhat made up for it. Overall, I’m just glad to have gotten through the test, and have also come up with a plan of attack for what I’m going to do, going forward, which I’ll get into at the end of this post. Plus, slow progress is better than no progress!

I started the week on the 14^th question of the 30 question test. I screen-shotted ten of the questions I worked through, some of which I got correct and some I didn’t.

Question 1

I had no idea what to do on this question so I picked a random answer and happened to choose the correct one. 🙄 I think the laymen’s explanation of what’s going on with math is that the height of the line integral (a.k.a. z) is equal to f(x,y) = (xy)^1/2. The length of the line integral is found by first finding the derivatives of the x– and y-functions which are both parametrized with respect to t which means you can then combine the derivatives and throw them into an integral to find the sum of the length of the line. (I’m very confident that what I just wrote made no sense.) I believe you have to find the absolute value of the derivative because the line could be going in the negative direction. I watched the following video after answering this question that I’ve seen a handful of times which helped to refresh my memory of what’s going on: 

Question 2

I got this question correct, as well, but also cheated on it. I watched the video below before working through the question which gave me the equation for a surface in 3D. Once I knew the equation, doing the algebra to solve the question wasn’t difficult.

Question 3

The only reason why I screen-shotted this question was because it was one where I quickly and easily was able to solve it on my own which I was pumped about.

Question 4

I can’t remember but I don’t believe I cheated on this question, but I also don’t think I solved it completely before answering. (The note I wrote out above was one I redid after scribbling out some math of what I thought was the solution.) It took me a minute but I remembered I needed to find the cross product of T_u X T_v, although I didn’t remember how to set up the cross product. I Googled it and remembered that î, ĵ, and k̂ needed to go in the top row. From there, it took me a second but I remembered that I needed to square the terms and then put them under a radical. That said, I partly only figured that last part after looking at the given solutions. 🤷🏻‍♂️

Question 5

I could have gotten this question correct but didn’t. My instinct was to find the partial derivatives of f and then figure out where each partial derivative equalled 0, which was the correct thing to do, but for some reason I just decided to input (1, 0) and (–1, 0) into the given function which resulted in it equalling 0 both times which made me think those were the correct solutions. Stupid…

Question 6

Again, this was another question that I was able to solve pretty easily which I was pretty pumped about. No real reason to add it here other than to give my ego a bit of a boost.   

Question 7

I got this question wrong and didn’t know what to do as I was trying to solve it. After looking at KA’s explanation, the math isn’t that difficult. I’m pretty sure I understand how and why the linear algebra works. I’m a little less clear on limits, in general, but have a vague understanding of why they’re used and feel pretty comfortable with the algebra used to get to the solution, 2.

Question 8

I didn’t cheat on this question and got it correct. Boom. 🧨

Question 9

Again, didn’t cheat, still got it correct. Double boom. 🧨 🧨

Question 10

I actually did cheat on this question by running it through Symbolab, but I would have gotten it correct even if I hadn’t. This question is a good one to indicate to myself that I can do ‘basic’ multivariable calculus questions (i.e. I know how to use the partial derivative and partial integral operations), so I’ve got that going for me which is nice. I just don’t understand the big picture of why a lot of the math works the way it does. 😒

Having got so many questions wrong on the Course Challenge, it now says I’ve only completed 94% of Multivariable Calculus (1,500/1,600 M.P.) and I will have to go back and redo four of the five unit tests in order to get the M.P. back up to 100% in those units. My game plan going forward is instead of doing that right away, I’m going to get started on the Linear Algebra course and will then do the Differential Calculus course before finally coming back to Multivariable Calculus to finish it off. I feel like doing it this way will help for a couple of reasons. First, I’ve found M.C. super difficult and confusing, and my lack of progress has been quite demoralizing and unmotivating, so starting a new subject will likely be a good change of pace for me. Second, I don’t feel like I have a great understanding of how to do linear algebra which is clearly used a TON in M.C. so going through that subject will make multivariable calculus SO much easier when I do get back to it.

I’m disappointed that I did so poorly on the Course Challenge, partly because it means finishing off the Math section on KA is going to take even longer that I thought it would. Nonetheless, I’m making progress and KNOW that I’ll get there eventually. Fingers crossed it’ll happen before 2026. 🤦🏻‍♂️ 🤞🏼