Recent content by PingPong

If you can show that A_(n+1)<A_n for n greater than some value, then it's decreasing for large enough n - which means its monotonic.

Right! Just one minor point, you're integrating with respect to u, so it's actually 4 ln |u| + u, not x :)

Be careful! (u)(1/u)=1, not u^2.

Try breaking up your numerator (i.e. (a+b)/c = a/c + b/c).

Okay, let's try to go slow. If you don't understand what I'm saying, let me know what doesn't make sense. There's not really just one formula you can use, it just takes some reasoning out. If \sin(\theta)=1/2, then what does \theta have to be? Either \theta=30 or \theta=150 (remember...

Try multiplying the numerator and denominator of your expression by the complex conjugate of the denominator (that is, x-1-i y). What happens?

Okay, so let's consider your problem now. First, look at the sine values. This gives a few possibilities for theta, namely pi/6 and 5pi/6. Which of these values of theta give the appropriate cosine value? Your second part looks good! EDIT: Whoops! Sorry, forgot you were dealing with degrees...

Your formula there should work for the top and bottom faces of the cube. But your front/back, left/right sides might pose problems, because their normal vectors don't have a k component. I think you might want to consider using the general flux formula: \Phi=\int\int \vec{F}\circ\hat{n}dS...

I think you've got issues with your math (at least, they're not showing up on Firefox for me). Can you retype your sine and cosine values?

I think you may be making the monotone part a bit too complicated. Look at x_{n+1}/x_n. What can you tell about this ratio? For the bounded part, why try to look at an upper bound for the numerator and a lower bound for the denominator?

Homework Statement Show that two matrices that have rational entries and are similar over the reals are also similar over the rationals. (Hint: Consider the polynomials from the rational canonical form over Q. What happens when we consider A as a real matrix? Homework Equations Rational...

Homework Statement Below is a sketch for a proof that for any distinct points A and B, there is always a point X between them: Take P not on \overleftrightarrow{AB} and Q with P between B and Q. Now take R with Q between A and R. The Pasch axiom shows that \overleftrightarrow{RP} crosses...

Hi, I'm not actually an electrical engineer (shh!) but I'm trying to do some circuit design to save our lab a little bit of money. We're looking to count triggers from a discriminator in a NIM crate. I've put together a prototype pulse counter on a bread board using some 74190 divide by...

Homework Statement Suppose there are two polynomials over a field, f and g, and that gcd(f,g)=1. Consider the rational functions a(x)/f(x) and b(x)/g(x), where deg(a)<deg(f) and deg(b)<deg(g). Show that if a(x)/f(x)=b(x)/g(x) is only true if a(x)=b(x)=0. Homework Equations None The Attempt at...

"Derivative" in an abstract polynomial ring Homework Statement Let R be any ring and define D:R[X]-->R[X] by setting D[\sum a_nX^n]=\sum na_nX^{n-1}. a) Check that, if f(X)=\sum a_nX^n and g(X)=\sum b_nX^n, then D[f+g]=D[f]+D[g] b) Check that...