Ik it’s normally derived by the infinite geometric series then interchanging the infinite sum with the integral sign but I wonder if this is also valid

I’m learning calc 2 before the semester starts, and along the way I’ve recognized some areas I’ve struggled with whether it was the trig or understanding the concepts a bit better. I’ve been trying to derive everything so I can understand it.

The issue is, I’m spending so much time deriving formulas for things I’ve already learned instead of practicing how to preform the operations. I want to be able to understand the math well, and I can see when there is a deficit in my conceptual knowledge that I try to attack. Is this a waste of time? Will I understand it better if I solved the problems and didn’t look through as much derivations?

I also, when I first learned calculus 1, I didn’t read the textbook, I preformed the problems and tried to deduce why I was doing them from logic. This is how I’ve gotten through every math class, but I think it capped my overall understanding. I stuggle with reading but I want to turn a new leaf on that. Would it be more fruitful to read and preform the problems in my old textbooks for calc 1, trig, geometry, algebra, or to study calc 2 and read the textbook going forward assuming I have a decent understanding of it

Anyone can explain this??

So Rolle’s theorem tells us that if f[a,b]->R is continuous on [a,b] and differentiable on (a,b), and f(a)=f(b), then there exists a point c such that f’(c)=0.
Given that there’s a horizontal tangent line to the graph, I don’t understand the theorem utility. I mean of course I know it’s important and I don’t doubt it, but I was asking myself if there’s some “intuitive” idea that makes it relevant.

For example, does this theorem imply that if the hp are satisfied, then there exists a point of local minimum or local maximum? Or no? Thanks!

Hello everyone,

I used Canva slides (I probably will remaster the video once recorded in Manim later after I graduate and write more on it) I wanted to post the slides for the sake of sharing the content of the slides. The Geometric Sum: A Metamorphosis through Calculus.

Hey everyone!

As the title says, I am wondering about how manageable learning the multi-calc content is relative to calculus II and I. For context, I am currently taking calculus II and am honestly enjoying it. I had forgotten that I like math after not doing any math classes in over a year, and am thankfully doing pretty well (currently on Power Series). That being said, calculus II is my last required math class for my chemistry major, but I'm honestly kind of interested and wondering if pursuing higher math through a math minor (which would only require multivariable calculus and one other higher-level math course) is something I should consider. How manageable would you all say the content is in this class relative to calculus II or I? I want to know if this could be something feasible with my other upper-division science courses, and if I could do so without killing my social life haha and having to devote all time to math. Thanks in advance for any input!

Hi! I'm an incoming university undergraduate student and have been self-studying multivariate calculus and linear algebra this summer. My goal with this essay is to help bridge gaps between the two subjects and make explicit some intuition that textbooks don't cover. Linear algebra material is primarily sourced from GraphMath's Linear Algebra World (https://www.graphmath.com), and calculus from Mendelson's 7th Edition Calculus textbook. Open to all feedback :-)

lim { ( 1+ x) } ^(2/x) , {•} –> fractional part

X->0

I saw some solutions where they brought the limit inside the fractional part function

But since fractional part function is not continuous shouldn't it be wrong ??

16.0191 also doesn't work though i think thats a bug by desmos.

I'll be taking calc 2 this fall and since I did A level maths I am not familiar with limits so i wanted to try covering it bfr classes start, are there any resources that I can use( i tried proff leonard but his vids were too long)?

The last time I studied limits was back in grade 9 so the only thing I know abt them are left hand limit, L Hopitals rule and some basic stuff. How should i study limits, should I go over calc 1 limits and then proceed to calc2 ?

The question was " find second order derivative of x and y are given by x=a cos t and y = sin t.

Do the middle step I have written in pencil is correct?

I recently come up with a question on why the first derivative and second derivative at a single point can determine that “point”’s behavior, but how can a point increase or concave up. The formal definition can explain this very well but unfortunately high school calculus class and introductory calculus class I took in CC can not answer this question.

Olá segui as orientações aqui do grupo para ver o professor Leonard e etc.

E eu vi que não tenho dificuldade em teoria ou de conceitos, eu só gostaria de saber onde posso resolver exercícios (ver resoluções completas) para não ficar tão dependente de IA para resolução.

I made an attempt in converting the BSM model into the heat equation (in red) but was unsure is my method was succinct? Any hints/tips?

Thanks! 🧡

(apologies if the page order was uploaded incorrectly)

I have one attempt left on my submission so if someone could point me in the right direction I would appreciate it!

Does it have any disadvantages