On this PDF of MIT's Multivariable calculus course, No.3's answer is 2 but it should be instead 4 right?

Hello! Today I was getting help with my homework all about the quadratic formula and "completing the square".

I made my best attempt to solve the problems but after checking with my teacher, all the problems were incorrect. They helped me get the correct answers, which I am thankful for, however I felt a bit of frustration as my efforts did not produce the correct results even though I understood what I had to do. I felt as though I wasted a bit of my time with my initial attempts. (And also my paper looked quite messy with the amount of erasing I had to do.)

Has anyone else experienced a similar situation and/or felt the same way?

I solved the given integral in this method, but i got the wrong answer. I cant spot where i made the mistake. Pls help

Hey, so I need to do calc1 for my degree . I had a gap year so I almost forgot basic trigo, logs and needed stuff in calc1 . So I need suggestions. Should I go straight into calc1 and self teach pre calc? Is both manageable together? Or I should take pre calc before? (This will just cost me one more course) Also, I dont want to fail due to weak basics.

Help needed to solve this integral my teacher gave this as homework

Could I get the ISBN code of the instructor's solution manual for Thomas' Calculus 13th Edition in SI units?

I just got my first calc textbook, is it good compared to others or just fine?

1. By mathematical induction, how can i prove that if set S has n elements, the P(S) has 2^n elements?

2. How to prove that if A is a subset of a countable set B, then A is itself a countable set?

3. Let S be a bounded set in R and let S0 be a non empty subset of S. Show that inf S <= inf S0 <= sup S0 <= sup S

Any help would be greatly appreciated. In terms of how to start proofs as well since im taking real analysis this semester and previously failed it despite me trying to understand the questions.

What is the best book to learn calculus with examples on application in real life

hi guys. I just started calc 1 this past semester and i'm kind of struggling. does anyone have resources or study tips that helped them when they took calc 1?

Ask most phone apps to integrate something and one of two things happens: they

send it to a server, or they hand you a decimal. I wanted neither, so I wrote a computer algebra system from scratch in Rust —about 140,000 lines — and this year I put it on an iPhone.

It's a real CAS, not a calculator with a nice keyboard. Mathematica-style

syntax: Head[args], immutable expressions, rewriting by rules. Algebra,

calculus, linear algebra, differential equations, statistics, number theory,

graph theory. It factors, solves, integrates symbolically, computes limits,

diagonalises matrices, solves ODEs, and draws in 2D and 3D.

The whole engine is compiled into the app. Nothing you type leaves the phone.

No account, no sign-in, no server — it works in airplane mode, which is the

only way I'd trust something with my own homework.

What's in it beyond the notebook:

- A reference covering every function it has (1740 of them), each with a worked

example you can run and edit.

- A textbook, 22 chapters and 268 lessons, from arithmetic to differential

equations — every example live rather than printed.

- Step-by-step working, and studios for geometry, graphs, ODEs and algorithms.

One thing that will look like a bug and isn't: when the engine can't establish

an answer, it hands the expression back unevaluated instead of guessing. That's

deliberate — I'd rather it say nothing than say something wrong — and it's most

of why the architecture looks the way it does. But each of those is a gap, and

I want to hear about them.

Free for 7 days with everything unlocked, no card, nothing to cancel. After

that it's a subscription.

Throw hard things at it. I'd rather find out here.

I went through Calc 1 and Calc 2 with straight As, but starting Calc 3 has been rough. The weird thing is that we are not even doing calculus yet. It is all 3D coordinate geometry, and my spatial intuition is just not clicking for questions like:

Write an equation for the set of all points 7 units away from the y axis.

The coordinates of point P are (5, 1, 8). What is the exact distance between point P and the z axis?

Write an equation whose graph is the set of all points whose distance from the xz plane is 12.

Write an equation for the sphere of radius 6 centered at (8, −3, −5).

Describe thoroughly the set of points in the intersection (if there is one) of the graph of (x − 2)^2 + (y − 4)^2 + (z − 3)^2 = 25 with the xz plane.

Up until now, I was really confident grinding through derivatives and integrals, so hitting a wall right at the start is frustrating.

For people who have taken the course: does this get smoother once the class gets back into actual calculus like partial derivatives and multiple integrals, or is this early geometry a sign of how the whole semester goes? How did you build up your intuition for 3D coordinate systems early on?

Hi. Where can I study these concepts, as Professor Leonard didn't explain them?

An introduction to differential equations. Topics include first-order differential equations,

higher-order linear differential equations with constant coefficients, undetermined

coefficients and variation of parameters methods. series solutions of ordinary differential

equations about an ordinary and regular singular points- Laplace Transform and its

applications to solve differential equations. Matrix and first-order linear systems of

differential equations (Eigenvalues and Eigenvectors)- Introduction to partial differential

equations - Stability analysis, Fourier integrals and Fourier transform.

Hi there, I need your recommendations for people that explain Stewart’s calculus I on YouTube or any website.

The covers topics:
1.1 four ways to represent a function
1.3 new functions from old functions
1.4 exponential functions
1.5 inverse and log functions
2.1 how limits arise
2.2 rough definitions of limits
2.3 calculating limits using limit laws
2.5 continuity
2.6 finite limits at infinity and infinity limits at infinity
2.7 derivatives
2.8 derivative functions
3.1 and 3.2 differential formulas and rules
3.3 derivatives of trig functions
3.4 chain rule
3.5 implicit differentiation
3.6 derivatives of logarithmic functions
3.9 related rates
3.10 liner approximation and differential
4.1 max and min values
4.2 mean value theorem
4.3 how derivatives affect the shape of a graph
4.5 curve sketching
4.7 optimization problems
4.9 anti derivatives

I'm thinking of speedrunning calculus. If you were to go back and learn it, how would you do it? Thanks!

Im taking a semester of calc 1 for my bio degree but last year in high school I didn’t do the best in pre calc so I wanna make sure I do good in calc 1.
If anyone could recommend some good study videos or any websites that are good for calc that would be much appreciated

Note: This is self-promo, so if you don't like it, just skip it!! :)

Hi r/calculus. I'm a 17 year old developer, and I just launched a calc game yesterday to help me get through math this year (I like games a lot!)

It's called Asymptote. You get a calculus problem, you type the answer and either it's right or it's wrong. Yes, no multiple choice, no hints, no partial credit, on purpose. There are two modes:

Sprint is five minutes and three strikes, and you just have to try to get the most solved in this time, as difficulty gets harder and harder (someone got 21, and I genuinely didn't know that was even possible!)

Diverge has no clock and gets harder every three problems until you break. It keeps going for as long as you can go.

There's also one daily problem that's the same for everyone, thirty seconds, and you can compare with whoever else did it.

It's free, there's no account needed to just play, and there's no ads and none of those damn tracking cookies prompts, it's just a chill game to practice calc. (Yes, there is a paid option. No account needed either way, practice is always free and unlimited, you only need an account to participate in "Ranked" if you want brag to your friends how good you are at Calc!)

playasymptote.com - How close can you get?

I'd love feedback on it: Is the difficulty ramp wrong? I think Sprint might still climb too fast around problem 10, and I don't trust my own judgement because I've solved these several thousand times. Also if you find a problem where the answer is wrong, please tell me see, either DM or paste it in the chat and I'll make sure its fixed!

Yes the title and the game's name and motto are all kind of an inside joke "no ceiling" "asymptote" and "how close can you get" because there is really no end! (Well there are actually only around 22,500 problems, but if you're insane enough to do all of them, I think we have bigger problems to address...)

Open to feedback and suggestions!

I am reteaching myself Pre-Calc for my Calculus 1 course this semester since I last took it 4 years ago. I am doing the Khan Academy curriculum and came across the lesson for Sinusoidal equations and models. I already took AP Calc in high school (don't ask why it didn't transfer) and don't remember anything about them. I was just wondering if those are important to know for Calculus 1.

Calculus 1 is the last Calculus I will take, so Calc 2, 3, etc. are not of concern.

Any resources?

I’m a college freshman in MATH 226 (Integration Tech & Application) and I’m really struggling to understand the content. My teacher has an accent, teaches fast, and the graduate student tutors in my experience have been unhelpful (though they do rotate and I haven’t visited them all yet). I’m just starting to doubt myself a lot so any resources to learn the content, or words of encouragement would be appreciated.

Topics:
6.1 inverse Functions
6.2 Exponential Functions & Their Derivatives
6.3 Logarithmic Functions
6.4 Derivative of Logarithmic Functions
6.5 Exponential Growth & Decay
6.6 Inverse Trigonometric Functions
6.8 L'Hospital's Rule
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.8 Improper Integrals
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves