Recent content by NanoMath

Thank you for replies. Actually I only needed to check that the whole expression goes to zero and multiplying and dividing through by K(t) solves it.

In the book from Evans on PDE's (page 48) I came across this integral. Here r > 0 and \delta is an arbitrarily small number. Could you give me some hint on how to solve this integral for all integers n\geq2 , i.e why does it go to zero as t approaches zero from the right side.

Homework Statement Given the force ## \vec{ F }(x) = (-12x + 6) \vec{i} ## ; find kinetic energy ## T## at the point ##x=2## and trajectory of a particle ## \vec{r}(t) ##, given that ## \vec{r}(t=0)=\vec{0}## and ##\dot{\vec{r}}(t=0)=\vec{0}## . 3. The Attempt at a Solution Since...

I managed to show that function is not surjective with the hint that every element in the range is of the form ## a+b \sqrt{5} ## because for example ##\sqrt{2}## doesn't get hit by any element in domain. Is it also valid argument that function can't be surjective because ##\mathbb{R}## is...

Homework Statement Hello guys So I have the following problem, given the mapping above I have to check weather it's ring homomorphism, and maybe monomorphism or epimorphism. The Attempt at a Solution So the mapping is obviously well defined, and I have proven it's homomorphism, and it's...

Would it be okay to take sequence an = √2/√nπ . Then this sequence obviously converges to zero as n goes to infinity. But f(an) alternates between 1,0,-1,0,...

Right so the first term cancels and I am left with: y sin ( 1/ y2 ) + sin ( 1 / y2 ) . So what do I conclude by taking the limit of this? y sin ( 1/ y2 ) vanishes since y goes to 0. I am a bit confused on what to do with sin ( 1/y2). Can I claim that limit doesn't exist because sin ( 1/ y2...

Homework Statement I have to show that the following function does not have a limit as (x,y) approaches (0,0) The Attempt at a Solution I tried taking different paths for example y=x or y=0 and switching to polar coordinates, but I don't get anywhere.

Thanks a lot for answers.

I'm sorry. Here you go.

Hello. In the proof of uniqueness of ( multi-variable ) derivative from Rudin, I am a little stuck on why the inequality holds. Rest of the proof after that is clear .