r/calculus

finally finished my calc 1 unit 1 course notes

(also included here are ε-δ proofs, proofs, squeeze theorem bounds, and piecewise discontinuity)

Older textbooks are better according to this YouTube short made by Wrath of Math. Edit: I couldn't embed the video. Here it is: https://www.youtube.com/watch?v=3o3zcMTBPZc

Is this still the case for someone trying to learn calculus independently?
I've learnt trigonometry and pre-calculus independently, merely by YouTube videos and practice thereafter.

But now I'm really struggling to just watch videos on YouTube to learn Calculus.

I couldn't find an appropriate flair, so I chose one randomly!

Hello guys, I was making my math activity, then i noticed something, how do i solve this?

Its a continuity problem wherein i need to find out if the function is continuous or not. However, the given piecewise function is overlapping, resulting in defined answer at the top while having defined answer on the bottom.

The second and third images are my proposed solution assuming the problem is true (its not)

hola a todos soy nueva en calculo intyegral y necesito ayuda mas que todo para saber si el proceso en general me queda bien y consejos de como hacer los ejercicios mas faciles.

Resultados (no se si me quedo bien)

1. 2/3 x^(3/2) + C

2. • 1/4x^4 + C

3. 9- 2Ln |x| - cos (x) + C

4. 3x^3 - 5Ln|x| + C

5. 2/3 x^(3/2) - 2/5 x^(5/2) + C

6. 3/13 x^(13/3) - 3/7 x^(7/3) - 6x^(1/3) + C

7. e^x + x + C

8. 2x^(1/2) + x + 2/3 x^(3/2) + Ln |x| + C

9. 5 Ln |sec(θ) + tan(θ)| -3 Ln |csc(θ) - cot(θ)| + Ln |sin(θ)| + C

10. • Ln |cos^2 (θ)| + Ln |sen^2(θ)| -2x + C

11. 4/7 u^(7/2) + 18/5 u^(5/2) + 8/3 u^(3/2) + C

12. -1/sin(θ) + C

13. 2x - 6 Ln|x| + C

14. 1/r2 arctan x/r2 + C

ACLARO quiero consejos para mejorar en este tipo de ejercicios, ya los resolvi por mi cuenta, no es una tarea, si los quieren usar para practicar ustedes haganlo :))

I took the radius of the shell as (2-y) because the distance formula is r = √(-2-(-y))² on the interval [-1, 0] of y. Is it right to choose -y because it is below the x-axis?

https://dailyintegral.com/play/derivatives/medium

For context, I went through Calc III like 10 years ago, and am in the process of refreshing my knowledge. Currently feeling comfortable with Calc I again, and starting again on Calc II.

The domain of this function contains pi as a single point, but it is not differentiable for that same reason (it's a single point).

Still, I thought it would be a fun challenge, so I differentiated this function by hand, and checked on Desmos that I got the right answer.

So I entered "undefined" into the site, and it said I'm wrong.

Am I missing something from higher level Calculus courses? Or is the site wrong/misleading? Hoping to learn here.

How does (d/dx)^2 equal second derivative? I can’t see the logic behind this. I know it says operator but I think it as the square of first derivative, not the second derivative.

Source: ChatGPT but explanation is confusing

For part (d) of my attempt seen attached, I believe based on the definitions and context in the document, $X_t = \int_0^t W_s \, ds$ is both, depending on how you view it:

• It can be treated pathwise as a Riemann integral: For each fixed sample path $\omega$, $W_s(\omega)$ is a continuous function of time, so the integral $\int_0^t W_s \, ds$ exists as a standard Riemann (or Lebesgue) integral.

• It is also an Itô process: As shown on the second page, its differential is given by:

$$d\left(\int_0^t W_s \, ds\right) = W_t \, dt$$

An Itô process is generally defined as a process of the form $X_t = X_0 + \int_0^t \mu_s \, ds + \int_0^t \sigma_s \, ds$. Here, it has a drift term $\mu_t = W_t$ and a diffusion term $\sigma_t = 0$ (meaning it is a special case where the stochastic differential term $dW_t$ has a coefficient of zero)

Therefore it can be viewed as both?

And polar coordinates are still trig integrals. Trig sub was goated too. I miss these. I just didnt like asymptotics

I want to self study the whole US calculus 1 - 2 would love some real analysis but not necessar, I kinda hate thick books like Thomas or stewart or apostol so courses are better for me or short books.

I’ve done the above topics in calculus not sure if they land in calc 1 or calc. 2 it lacks limits and other advance things, it’s the IAL mathematics pure 1-3 textbook(highschool).

Is there a newer MIT scholar OCW ? the lectures are hard to read in the videos for example “what’s written in the blackboard”.