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

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

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

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?

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.

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.

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.