Recent content by jakncoke

yea, if A, B are nxn invertible then AB is invertible. Since Matrix Multiplication is associative, (AB)C is invertible provided c is nxn invertible.

By a zero sequence do you mean its like {0, 0, 0, 0, 0...} or it converges to 0 as n\rightarrow\infty

Applying integration by parts which states \int u\frac{dv}{dx}\,dx = uv - \int v \frac{du}{dx}\,dx u=ln(x) and v=x So \int ln(x)\,dx = xln(x) - \int x\frac{1}{x}\,dx = xln(x)-x+c

A) Basis spans your subspace. So your answer indicates, for example that, \left[ \begin{array}{cccc}0 & 1 \\ 1 & 1 \\ 1 & 0 \end{array} \right] x = \left[ \begin{array}{cccc}0 \\ 2 \\ 5 \end{array} \right] should have a solution, but under ur basis, this eqn has no solution. so ur basis...

Your part where u show the base case is correct but u can't just replace k with k+1. otherwise it would be a tautology not a proof. you have to show you can get it into the form where 1+1/4+1/9+...+1/k+1/(k+1) <= 2 - 1/(k+1) Here is a simple proof: Show by induction that 1+2+3+...+n =...

Let E be a proper subset of R. There is a point p not in E s.t for any e>0, there exists a point q in E s.t |p-q|<e. Prove that E is not compact. Proof: p is in R-E. For a e>0, p+e is in E. So R-E is closed on one side which implies E is open on one side. By using heine-borel thrm we can...

Homework Statement Clepsydra was a water clock used in old times in which water was allowed to espace through a small hole at the bottom. Find the shape of the clepsydra, if the water level is to fall at a constant rate. Homework Equations Torricelli Law The Attempt at a Solution...

Homework Statement supposed to prove informally that f(x)=Integral 0-->infinity (cosxt/(t^2+1))dt == Pi/2*Exp[-x] Homework Equations The Attempt at a Solution no clue, need some hints to get started

since z=y/x d/dt(z) = d/dt(y/x) == dz/dt = 1/x dy/dt - y/x^2 dx/dt we know dx/dt = 3ft/s we know dy/dt = dy/dx*dx/dt u know x^2+y^2=24^2

yes.

F base xy means differentiate with x while keeping y constant, then take the rest and differentiate with respect to y keeping x constant. example: f(x,y)= 3x^2+2xy f(x,y)x = 6x+2y f(x,y)xy = 2

right side means that u are supposed to integrate with respect to x -Integrate[1/x] with respect to x

cosh x = (Exp[x] + Exp[-x])/2

agree with what grief said, one more hint. Chain rule!

are u sure this is the right differential equation? u get Y =~\int cos(x^2)e^{sin(x)}dx but i enter the right side in mathematica and get no result