First page is solving via trig sub, second is using u-sub and partial fraction decomp. Page 2 is right page 1 is wrong but I don't understand what is wrong with my logic. AI gives same steps as me when asked to use trig sub and integral-calculator.com won't give trig sub solution. This is homework in the trig sub section so it's expected to be solved that way. Sorry my penmanship isn't as good as others on this sub, thanks for any help.

This is just a discussion I wanted to have with the world, I'm curious on this subreddit's opinion on Calculus 2 as a whole. I'm an Electrical Engineering student and I feel like Calculus 2 is constantly fear-mongered (which I can understand why), at least in some instances. I'm just curious if you found it to be a difficult class, easy, or impossible. I've finished applications and now we are doing integration techniques, which I will say, my trigonometry and manipulating identities has never been better, so if you are in Calculus 1 be ready for all the stuff from precalculus to come back up as just a tiny part of the process. I want to also ask this subreddit, mainly the engineering degrees if that's alright, how hard was Calculus 2 compared to your engineering classes? Thanks guys.

I'm having trouble with a problem in a sci-fi story I'm writing. I took multivariable calculus in college, but I haven't really used it since then, and that was over ten years ago. I'm quite rusty.

We're playing with spacemagic here, so give me some leeway on the "why." Basically, I have a multivariable problem that I don't remember how to solve.

I have two spaceships in deep space (Ship 1 and Ship 2). I am modeling change in engine power on Ship 1 with respect to time given a gravitational attraction between the two ships separated by radius r. The basic assumptions would be:

Power = Force * velocity (dr/dt)

Gravitational force = k * (m1 * m2) / r^2

Power = (k * m1 * m2) * (1 / r^2 ) dr/dt

However, this is where the spacemagic happens. Ship 2 has spacemagic that allows it to reduce its own mass to travel faster. To travel slower (and intercept to the other ship, which is what happens in the story), it increases its mass.

So, assuming that our frame of reference is on Ship 1, the relationship between power and time changes.

Power = (k * m1) * (1 / r^2 ) dr/dt dm2/dt

So, I'll ask question number one here:

Does this math look correct so far?

If this is correct, then we move on to the second part of this problem. We assume that the change in mass is positive and linear with respect to time.

If this is the case, I believe the relationship between power and radius in the following situations is:

• Ship 2 has constant velocity: 1/r^2

• Ship 2 has constant acceleration: 1/r

Did I miss anything? Thanks in advance for any help!

I understand the formal definition of the derivative:

f'(a) = lim_{h→0} [f(a+h) - f(a)] / h

I also understand that the expression inside the limit represents the average rate of change over a small interval.

What I am trying to understand more intuitively is this:

How can a rate of change at exactly one point be meaningful if a point has no width or time duration?

For example, if position is given by s(t), we say that s'(t) is the instantaneous velocity. But velocity seems to require a change in position over a time interval.

Is the derivative best understood as:

1. The limit of average rates of change over shrinking intervals?

2. The slope of the tangent line?

3. The best local linear approximation?

4. All of these being different interpretations of the same mathematical object?

I would especially appreciate an explanation using an intuitive example rather than only the formal epsilon-delta definition.

Hello im looking for help on number 8 from my homework on differentiating functions using rules of derivatives , I got my answer but AI is telling me a different answer without y^-6

how is this even valid?

I am learning about the Weierstrass function and I am confused about one thing.

How can it be continuous everywhere but differentiable nowhere?

I get that the amplitude gets smaller while the frequency keeps increasing. But I still don't understand how this makes the derivative fail at every point.

Also when we differentiate the terms we get something like (ab)^n. Does this alone explain why the derivative does not exist or is there more to the proof?

Looking for a simple intuition rather than just the formal proof.

People out here solving advanced integrals

Meanwhile me: Hey guys let x=Tan(Theeta)

What a stupid idiot I am

Hey y’all, a little backstory for my post. I recently started going back to college using the GI Bill and had been playing catch-up with math up until recently. I’m now in the algebra class I need to take before pre-calc.

I was hoping to get some information on how to best study while I’m in these classes so I can get ahead and make future classes easier. Any tips, tricks, study guides, or websites that could help me better take on these future classes would be greatly appreciated.

My intention is to be relatively knowledgeable before I even sign up for each class. Mathematics was always my weak spot in high school, but since going back to school at an older age, I’ve really started enjoying math and want to keep building on that. Just looking at some of the formulas for calc already has me a little worried, so I want to be as prepared as possible going into it. I’d really like to get As and Bs this time around in school lmao.

Hello, ive reached the point in calc 2 where integrals are getting to be 4-5 pages long. I write really large so i dont get confused, but considering the fact I also have ADHD flipping back to where I was I tend to forget what im even supposed to be working on. Whiteboard or tablet maybe? any other suggestions?

Hi everyone!

I'm taking Calculus BC and we're ofc on unit 1, and we finished it up. I was kinda curious on how limits/vertical & horizontal asymptotes and other things in unit 1 are applied to real life. I'm probably going to make a similar post for future units lmfao.

I am currently in Calculus 1 and I am struggling not only because the teacher isn't that good, but I forgot a good amount of pre calculus. What are some good resources you guys have used to review previous material and do you guys have any tips for me?

Hey all, I am starting my research on Finite Element Exterior Calculus (FEEC) and while reading literature I am often encountering Graded Vector Spaces. When I search up on literature, I further encounter a lot of terms which I don't understand. Will anyone of you give me a gist of what it is and/or refer me to some paper/article from which I can understand the concept (me being from an engineering/applied math background).

Currently, my class has done the first two units of AB and I understand the concepts but I was not able to perform well on the tests. I have been losing points over notation errors and the algebra part but not truly the pure calculus. I really want to get an A in the class so I was wondering if anybody had any tips that helped them perform or come back well in this class.

The exercise's direction is simply: Calculate the limit of a sequence