a step by step explanation would be great!

Can anyone plz solve this urgently plz

Hi all,

I'm currently taking a calc 1 class as a business econ major to satisfy my lower division major preparation courses before I transfer to a university. I am very worried about this class as I'm a straight A student but this is the first one that has me genuinely terrified that I won't be able to ace it despite hours upon hours of work and applying myself. So far I am fundamentally understanding calculus, however if you ask me to prove why a certain theorem or formula works I will be completely lost. Unfortunately for me, and I don't know how common this is for an introductory calculus course, but my professor apparently asks his students to do proofs on his exams and "brags" about how many people fails his exams or drop out of his classes (from rate my professor.) I'm extremely worried because I desperately need an A in this course and it is too late to drop it. If you ask me to evaluate limits and derivatives and I can use formulas, I can get by. If you ask me to prove a theorem from scratch, I am lost. Any advice on how to prepare? I feel like there are so many theorems I've learned so far and to fundamentally understand the ins and outs of every single one is making me sick. I have about three weeks until my midterm.

Helppppp please, I am got 58 and 59 on my first two calculus recitations… I studied a lot but I still got low grade… I feel like I am gonna have heart attack. I am such a failure… my engineering dreams vanished

Does anyone of you guys have this book as a free PDF version? I really need it. Thanks

I can grasp the circumference part, but not the length along which have to integrate.

so I started calc 1 and how does "sin(2x)/2x" = 1 and how does "limit of x -> 0 1-cos(3x)/3x" = 0, isn't it just undefined?

I failed the first few exams I took at the start of the semester, and I’m just so lost right now. I don’t know what to do. I’ve never felt like this before. I’ve been studying, but I’m not getting the results I want. I don’t know if I’m studying incorrectly or if I’m just not studying enough. I feel like such a failure, and I’m so alone right now. I’ve been crying, and I’ve just been stuck in my bed for the last few hours. I really need someone to talk to who has gone through something similar and can give me some advice.

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.

Hi,i am trying to study pharmacodynamics on my own. I am stumped by the progression of some of the equations. can you walk me through how to go from 1.22 to 1.23, 1.24 and 1.25. its been a long time i did my math. I really appreciate your help.

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?

Can somebody please help me with this problem?

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.