Hello I'm having problems with actually proving this with some mathematics.
Let A, B, C be sets. Prove that if A is a subset of B and B is a subset of C then A is a subset of C.
Thanks.
Homework Statement
If \phi=a_{rs}x^{r}x^{s}
Then show that \frac{\partial\phi}{\partial x^{r}}=(a_{rs}+a_{sr})x^{s}
Homework Equations
The Attempt at a Solution
Help please I can't seem to get the correct answer. Thanks
I'm looking for a classical mechanics book that is heavily mathematical based, I've looked around a little however I'm lazy and don't want to buy a dud book. any recommendations would be great, thanks. (also i know there's 100000000000threads on text recom's however can't seem to find much ppl...
1) p(x)=-1, q(x)=4e^x & 2) p(x)=2x and q(x)=4 ( Just because there's no x doesn't mean its not a function of x, or of whatever independent variable your working with; its just for every x value u'll get the same f(x), which is obv since its constant. you can view it as f(x)=4x^0, whatever x you...
the problem is in your algebra, on the left you have, after differentiating, (x^1/2)4x, now when putting it over a common denom, you get 2x^1/2[(x^1/2)4x] which becomes 2x times 4x... from here i think u can finish it correctly
edit: or the way you've done it, (4x^3/2) which is the left, you...
Homework Statement
\underset{n\rightarrow\infty}{lim}\frac{e^{1/n}+e^{2/n}+e^{3/n}+\cdots+e^{n/n}}{n}The Attempt at a Solution
done something with Riemann sums however didn't get far, other than that I'm not to sure how to evaluate this. any help would be great, thanks (also not sure if i...