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...
Why would I put the y^2 into the equation and square the other side? And what is a "true equation"?
I have a feeling these will be on our exam next week, so I want to understand it well.
Thanks
Oh ok , I got it. I am in Calc 2 and when I read Diff. Eq. it just scared me off.
That was easy enough. It is a seven part question, and the third part looks very similar:
Show that for the arbitrary constants A and B, the function y=Atanh(Bt) satisfies:
\frac{dy}{dt}=AB-\frac{B}{A}y^{2}
I...
Homework Statement
Show that
y=tanh(t)
satisfies the differential equation
\frac{dy}{dt}=1-y^{2}
with initial conditions y(0) = 0
Homework Equations
The Attempt at a Solution
I'm not sure how to start, but we have only dealt with one D.E., and we had moved all the...
Homework Statement
\int\stackrel{tan(8)}{tan(1)}\frac{dx}{x^{2}+1}
Homework Equations
The Attempt at a Solution
\int\stackrel{tan(8)}{tan(1)}\frac{dx}{x^{2}+1}
tan^{-1}x|\stackrel{tan(8)}{tan(1)}
tan^{-1}(tan(8))-tan^{-1}(tan(1))
8-1=7
I'm fine with this, but my instructor said...
Homework Statement
Three point charges lie along a circle of radius r at angles of 30°, 150°, and 270° as shown in the figure below. Find a symbolic expression for the resultant electric field at the center of the circle.
Homework Equations
\vec{E}=\frac{k_{e}q}{r^{2}}
The Attempt at a...
I can get r in terms of x and d:
r=x^{2}+d^{2}
I guess I put that in the integral:
k\int\frac{dq}{x^{2}+d^{2}}
I know thats not right, I really have no idea, I'm giving up on this problem.
We have 12, all were super easy (variations of E=F/q) except this one.
I don't even partly understand...
Alright, so I have
k\int\frac{dq}{L^{2}}
My professor only worked one example, and it was used because it was symmetrical and most charges cancelled out.
I'm looking over the video he did, and he added a cos(theta) in the integral (his reasoning being "this needs to go here"). I'm...
Would I use
F_{e}=k_{e}\frac{q_{1}q_{2}}{r^{2}}
and
E=\frac{F_{e}}{q_{0}}
Thats the only equation we have that relates q and distance r, but I'm not sure what to actually plug in.
EDIT: I should plug in dq=(lambda)dL, where lambda is q/L?
Homework Statement
A uniformly charged rod of length L and total charge Q lies along the x axis as shown.
Find the components of the electric field at the point P on the y-axis a distance d from the origin.
There's also a part b but I should be able to figure it out easily enough...
Thanks a lot guys.
My teacher did say that we must use L'Hopital's rule to do it, but I got it worked out with a final answer of e^(-1/6) after exponentiation.
Thanks again!
I realize lim x->0+ needs to be in every step, but for the sake of my sanity I will leave them off in this problem (of course I will write it down on my hw though)
\frac{1}{x^{2}}ln\frac{sinx}{x}=\frac{ln\frac{sinx}{x}}{x^{2}}=\frac{lnsinx-lnx}{x^{2}}=indeterminate...
Uh oh, this doesn't seem to be right:
lim_{x\rightarrow0^{+}}(\frac{sinx}{x})^{1/x^{2}}
lim_{x\rightarrow0^{+}}(\frac{sinx}{x^{3}})=0/0
lim_{x\rightarrow0^{+}}(\frac{cosx}{3x^{2}}})=1/0
lim_{x\rightarrow0^{+}}(\frac{-sinx}{6x})=0/0
lim_{x\rightarrow0^{+}}(\frac{-cosx}{6}})=-1/6
To me...
Homework Statement
I need to find the limit of this using L'Hopital Rule, if it exists.
lim_{x\rightarrow0^{+}}(\frac{sinx}{x})^{1/x^{2}}
Homework Equations
All of our examples used lim f(x)/g(x)=f'(x)/g'(x)
The Attempt at a Solution
We have not dealt with any limits like this that have...