With CERN's Large Hadron Collider being in the news recently, I began to think of a question that bothered me for years about particle accelerators.
It is well known in physics that mass increases as velocity does (Special Relativity if I'm not mistaken), so if these particles in the LHC are...
Ah, ok, I got -1/6.
I don't remember why exactly I didn't get a good answer on the exam, but I think I was on like my 6th L'Hopital iteration and wasn't willing to spend any more time on a 4 point problem.
Thanks guys, now I can rest easy this summer, as my brain is completely fried now!
Homework Statement
I had an exam last night and I was stuck on this problem.
I went home where I had more time (and resources) and still can't figure it out, and I won't get my exam back (it was a final).
\lim_{x\to0}\frac{1}{x^{2}}-\frac{1}{xsinx}
Homework Equations
The...
Homework Statement
\int\frac{dx}{x(x^{2}-1)^{3/2}}
Homework Equations
The Attempt at a Solution
I know I need to use trig sub, but which form? I can't seem to find any that fit this form.
Never mind, I figured it out with a comparison test.
Funny, after I post things on here I always seem to figure them out on my own.
Well, whatever works!
Homework Statement
The gamma function, which plays an important role in advanced applications, is defined for
n\geq1 by \Gamma(n)=\int_0^{\infty} t^{n-1}e^{-t}dt
(a) Show that the integral converges on n\geq1
(b) Show that \Gamma(n+1)=n\Gamma(n)
(c) Show that \Gamma(n+1)=n! if n\geq1 is an...
101e5 tells me that I am off by a multiple of ten.
I am still confused though- in my calculator I put in
(K*6.75*10e-6)/6e-2
(I have K stored as the ke constant)
and get 101. It sounds like you're telling me that my calculator cannot handle scientific notation, and I need to tag on the "...
Homework Statement
Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much...
Ugh, this problem is killing me. On a later part, it asks:
Let v(t) be the velocity of a falling object of mass m that started from rest. For large velocities, air resistance is proportional to the square of velocity v(t)2.
If we choose coordinates so that v(t)>0 for a falling object, then...
Cool, thanks a lot.
I think I'm definitely ready for an exam on Monday.
EDIT: I had a math error on my last post when I substituted for y2. When done properly, all the A's cancelled out.
Oh ok I get it.
On part A I algebraically rearranged to get dy/(1-y^2 )=dt, then I integrated both sides to get (after simplification) y= tanht, done. Just did it the long way, not even thinking because all the other problems were integration.
then, when I started integrating part b...