Recent content by Anama Skout

If you could find a closed form for ##a(x)## then you'd be able to find any closed form formula for any primitive of any function, by putting ##f(x)=\ln g(x)## in your formula, but that's impossible by Louisville's theorem.

I started reading Baby Rudin with @VKnopp for some weeks, but unfortunately, I was confiscated any access to the Internet for many months, I'm only back now. Is anyone still interested in such a project?

No one mentioned Hubbard?

Also anhttp://www.uni-graz.at/~gronau/TMCS_1_2003.pdf that attempts to answer: "Why is ##\Gamma(n)=(n-1)!## and not ##\Gamma(n)=n!##?" Edit: Some other papers: Wladimir de Azevedo Pribitkin, Laplace's Integral, the Gamma Function, and beyond, American Mathematical Monthly. Gopala Krishna...

That's because $$\frac{1}{\cos x+i\sin x}=\frac{\cos x-i\sin x}{(\cos x +i\sin x)(\cos x-i\sin x)}=\ldots$$ Then use the Pythagorean identity. I would say: it isn't safe.

Here are some references I found out on reddit: (I don't know if that's advanced enough for your level) Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, by George Boros and Victor Moll. Chapter 11 deals with the Gamma and Beta functions. Paul Nahin...

What's the longest time antimatter was able to be stored?

I don't know, the magnetic field could affect the electrons and the results of the experiment, some ketchup wouldn't for sure

I just thought about this one, suppose we have the classic double slit experiment setting, and we add near the holes in the slits a strong magnetic field, what will happen? what if the magnetic field was only on one slit? What if we put that magnetic field in place (2) instead of (1), would that...

You can download the entire Book of Proof here: http://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf Or if you want individual chapters you may have a look here: http://www.people.vcu.edu/~rhammack/BookOfProof/ Part I & II & III are sufficient. Zorich already treats functions and...

For that exercise, no, just write the truth table of both the LHS & RHS and conclude. However I see that Zorich doesn't introduce proof techniques (e.g. how to prove a biconditional? how to make a proof by contradiction? how to make a proof by contrapositive? ...) Are you already familiar with...

Look at the Peano axioms. If you want a detailed reference on the construction of the naturals (as well as the rationals, reals..) check the celebrated Foundations of Analysis by E. Landau. I didn't explain how a proof by induction should be conducted, rather I explained why they are true I...

Straight from my physics textbook: For objects moving at high speeds through air, such as airplanes, skydivers, cars, and baseballs, the resistive force is reasonably well modeled as proportional to the square of the speed. In these situations, the magnitude of the resistive force can be...

My mistake, thanks, corrected

There's even a method to simply check for two cases only, by dividing both sides by ##|4x+2|##, $$\begin{align*}2|4x-1| = 3|4x+2|&\overset{\ ?}\iff \frac{2|4x-1|}{|4x+2|}=\frac{3|4x+2|}{|4x+2|} \end{align*}$$ Since we're dividing by ##|4x+2|## we must have ##x\neq -1/2##, so for the equivalence...