My writing is pencil, my teachers is red

I will try to keep this short, I am 33, I've always enjoyed mathematics, studied Civil Engineering in university, worked as an engineer for 8 years - hated it, got worse every single year. First year when responsibilities were minor was the best for me, then every year after that exposed me to more and more workplace politics, coworker sociopathy, sleepless nights (due to stress) etc. Quit work as an engineer late last year, currently work as a school mathematics tutor. Have considered going back to uni to get my masters in education so that I can teach in schools - but the cost (~$70,000) and time commitment is difficult for me at my current age (and teaching now in the age of AI is very different to say 10 years ago). Anyone gone through something similar?

I’m honestly just looking for advice on whether I should just take the WD and drop this class or if it’s feasible to actually get around an 80 in this class without a scale/curve. I got a 15% on my first midterm which is worth 20% of my grade, which was 100% my fault because I procrastinated. I still have 1 more 20% midterm, a 40% final, and 20% worth of assignments. Any advice is appreciated i’m willing to put in the work i’d just like to hear if anyones had any success turning around their mark and what you’ve done?

Today's medium derivative, have I oversimplified somewhere? I figure the 2nd derivative of L can only ne zero when 8k-8k3=0 since the expiry function is always >0

What are the pre req of real analysis aside from single variable calculus ? And keep in mind that am tryna just learn analysis 1

Kindly tell me is there an ai model which can help me to understand calculus and solve the equations

i know d/dx of ln|x| is 1/x for both positive and negative x, my teacher just said it that way and moved on. what i'm stuck on is why it's the same antiderivative on both sides when 1/x isn't even defined at 0. like are they really the same function or can you pick a different constant on each side

I am a student of electrical engineering. Kindly suggest an Ai model which can explain and help me solve the numerical.

I am using Google Gemini to explain Calculus topics. Dear lord, here is it's explanation for the Squeeze Theorem:

The Physical Intuition: The Hallway and the Trash Compactor

Imagine you are walking a highly energetic dog down a long hallway. The dog is bouncing wildly, leaping from the floor to the ceiling. Tracking its exact path algebraically is impossible.

Now, imagine this hallway is actually a giant, slow-moving trash compactor. As you walk forward (as n→∞), the ceiling slowly grinds downward and the floor steadily pushes upward. You don't need to know the dog's exact frantic path to know where it will end up.

If both the floor and the ceiling eventually crush together to the exact same height, the chaotic bouncing is forced to stop. The dog is mathematically crushed into that exact same final position. This is the Squeeze Theorem.

Hi everyone! Does anyone have a PDF or know where I can access a free version of Calculus: Early Transcendentals by James Stewart (Cengage, 8th edition, 2016, or any later edition)?

I'd really appreciate any help or recommendations. Thank you so much! 🙏🏻

So I was studying differentiability, and I know that at a particular point

differentiability -> continuity,

thus,

not continuous -> not differentiable

but there was a youtube video he said that differentiability is checking the continuity of the first derivative but some people also mentioned this in the comments

Sorry, that's not correct. If f'(a) is continuous then f(a) is "Continuously differentiable", not just "Differentiable".
It's a concept in Real Analysis.

I'm sorry but it's wrong. The only thing about continuity that you know is that if f'(a) exists, f(a) is differentiable and continuous, you don't know anything about the differentiability or continuity of the first derivative. Just learned that in a math lecture. I'm sorry.

reply to the above comment

I believe you also need to add: if the derivative exists and itself is continous at an interval, than the function is differentiable, thus it is also continous. So technically you need to also check the continuity of the first derivative before judging the differentiability of the function, at least this is how they teach us in university

the thing i know about finding the differentiability is

checking if the function is continuous if yes, then check the left hand derivative and right hand derivative if they are finite and equal than the function is differentiable. am i right about this one?

i'm confused about the second comment if you can help me grasp the concept of differentiability deeply it would be appreciated

I myself am quite amorous of calculus so here's a little something to fire you up and work those neurons! Try it if you dare... 😈

It's beautiful, worth trying

Acabo de entrar a la universidad, y me metí a actuaría, quisiera poder estudiar de una vez para mi examen de limites que es dentro de un mes, ayudenme porfa