Recent content by Duane

I had a bit of trouble in testing series like this for convergence $$\sum_{ n=1 }^{ \infty } \frac { 1 }{ 2n+1 } $$ If by the comparison test, ##\frac{ 1 }{ 2n+1 } < \frac{ 1 }{ 2n }## for all of n>0, and ##\lim_{ n \rightarrow \infty} \frac{ 1 }{ 2n }## =0, then the series should be...

Hi everyone I'm currently studying the MO theory and ran into some trouble understanding orbital energy levels. As I have previously read, σ bonds are stronger than ∏ bonds, therefore are lower in orbital energy. However, from the MO theory, the σ2p orbital is actually higher in energy than...

How do you graph f'(x) when f(x)= sin(x+sin2x), 0≤x≤∏ ? If I calculate f'(x) first by the chain rule, I get f'(x)=cos(x+sin2x)(1+cos2x), where to proceed ? Thanks for any help in advance.

Sorry I messed up. What I meant was a "rational" function. Are "rational" and "quotient" synonymous ? By applying the quotient rule, I get (ax+b/cx+d)'= [(cx+d)(ax+b)'-(ax+b)(cx+d)'] / (cx+d)^2 = [a(cx+d)-c(ax+b)] / (cx+d)^2 how to proceed ?

Hi guys I'm getting into a little trouble when differentiating polynomial functions. How do you differentiate f(x)=ax+b/cx+d ? Is there other ways of calculating this apart from the chain rule ? Thanks for any help.

Thanks, that helped a lot!

What is the physical meaning of each term in the parallel-axis theorem? I=I com +Mh^2