Recent content by lmstaples

Consider a beam of positive Muons, of energy 0.3GeV in the laboratory. (i) What is the apparent mean lifetime of the Muon as measured in the laboratory frame? (ii) What is the mean distanced traveled by the Muon in the laboratory? I first tried using the E = pc and working out speed...

Haha sorry, I had so many ideas of ways to do it and that's the only one I managed to fully work through :)

check out the attachment, does that seem right?

Homework Statement The line segment AB lies on a diameter of a circle of radius 1, and the angle BAC is a right angle. Find the greatest possible value of the sum of the lengths of AB and AC. Homework Equations The Attempt at a Solution I have no idea what parameters to use...

Would it not converge to 0 for any α >= 2

I believe I got it to reduce to [(x^2)^(α/2 - 1)][-cos(1/x)]

Well the sin term will tend to 0 but the cos term will oscillate like crazy

Looking back, as x tends to 0 the cos term must become irrelevant. e.g. If x = 0.000001, x >> x^2

Sorry in advance for lack of latex, on a mobile. Combining brackets gives us: [α(x^2)sin(1/x) - xcos(1/x)]/[x^3] I can't see how one term is particularly irrelevant. As for |x|^α: by all means use that notation, I only changed it as that particular function [F(x)] actually came from...

The main difference between the two terms in the brackets are: 1) the use of α in the sin term 2) the cos term is over a higher power of x Possibly the cos term is irrelevant due to it not depending on α which is what in looking for, for continuity. Or possibly the sin term is...

How do you do that for functions which have "two parts" to them? Also, as x starts getting close to 0 everything is going to go crazy because of all the dividing by x's. I remember doing a question a while back which was basically "is f(x) = sin(1/x) continuous at 0 if f(0) = 0?" I...

Homework Statement F(x) \ = \ (x^{2})^{\frac{\alpha}{2}} \left[ \frac{\alpha sin \left( \frac{1}{x} \right)}{x} \ - \ \frac{cos \left( \frac{1}{x} \right)}{x^{2}} \right] \ if \ x \neq 0 F(x) \ = \ 0 \ if \ x \ = \ 0 Question basically says, for what values of alpha is this function...

It came out perfectly :D

LATEX is very difficult on a mobile sorry :( Thanks for the mastery compliment :) As for how I obtained the result... WolframAlpha But it times out when you try to put limits from 0 to 1/cos(θ)

integral = -1/2 sec(2 theta) (log(r^2 (-cos(2 theta))+r^2+2)-log(r^2 cos(2 theta)+r^2+2))+constant