Recent content by mreaume

Homework Statement Find the sum of the following series: Σ n*(1/2)^n (from n = 1 to n = inf). Homework Equations I know that Σ r^n (from n = 0 to n = inf) = 1 / (1 - r) if |r| < 1. The Attempt at a Solution [/B] I began by rescaling the sum, i.e. Σ (n+1)*(1/2)^(n+1) (from n = 0 to n =...

Homework Statement Find the area of that part of the cylinder x^2 + y^2 = 2ay that lies inside the sphere x^2 + y^2 + z^2 = 4a^2. Homework Equations [/B] If a surface S can be parametrized in terms of two variables u and v, then dS = Norm[dR(u,v)/du x dR(u,v)/dv]. The surface area is given...

Homework Statement A solid sphere of brass (bulk modulus of 14.0*10^10 N/m^2) with a diameter of 3.00 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sings to a depth of 1.0 km? Homework Equations Gauge pressure = density(water)*g*h Bulk...

Thanks. Turns out I misread the question. I ended up using your tip (partial derivatives) and was able to solve the problem.

Homework Statement A function f is defined on the whole of the xy-plane as follows: f(x,y) = 0 if x=0 f(x,y) = 0 if y = 0 f(x,y) = g(x,y)/(x^2 + y^2) otherwise a) g(x,y) = 5x^3sin(y) b) g(x,y) = 6x^3 + y^3 c) g(x,y) = 8xy For each of the following functions g determine if the...

Well we can write 1+2+4+8+... as the sum from n=0 to n=inf of 2^n. And similarly we can write 1+3+9+... as the sum from n=0 to n=inf of 3^n. So can we say that the series is (2/3)^n? From n=0 to n=inf?

Homework Statement Determine whether the series diverges or converges. (1+2) / (1+3)+ ((1+2+4)/(1+3+9))+ ((1+2+4+8)/(1+3+9+27)) + ...The Attempt at a Solution I have split up the series into two (denominator and numerator): an = (1+2) + (1+2+4) + (1+2+4+8)+... = (1)n + 2n + 4(n-1) + ... bn...

Perfect. Thanks for your help!

Ok. Here is what I have: (A^2 -3A +2I) = 0 A^2v -3Av +2Iv = 0 AAv -3Av + 2v = 0 (c^2)v - 3cv + 2v = 0 (c^2 - 3c + 2)v = 0 ((c-2)(c-1))v=0 Therefore (A-cI) is not invertible when c=1 c=2. I think I understand now. Does everything seem to be in order in my procedure? Thanks for your help.

LCKurtz, I do not have the Cayley-Hamilton theorem available. It has not been presented in class yet. Dick, I have understood the following: (A-cI)v=0 So Av=cv I imagine that we need det(A-cI)=0 in order to prove that A-cI is invertible. I am stuck here. I don't know how to relate A^2 -3A +2I...

Homework Statement Prove or disprove the following statements. I and 0 denote respectively the identity and zero matrix of the same size as A. If A is a square matrix such that A^2 - 3A +2I = 0 then A-cI is invertible whenever c is not equal to 1 and c is not equal to 2. Homework...