Recent content by Isaac Wiebe

All ai ⋲ N, so yes they are. And for n = 2 I eventually receive that √(a1 * a2) ≤ 1/2 (a1 + a2) Or a1 * a2 ≤ [(a1 + a2)^2] / 4. Not entirely sure why I would want to do multiple base cases, but I think you are on the right track.

Homework Statement Show via induction that the nth root of (a1 * a2 * a3 * ... an) ≤ 1/ (n) * ∑ ai, where i ranges from 1 to n. Homework Equations Induction The Attempt at a Solution Let Pn be the statement above. It is clear that P1 holds since a1 ≤ a1. Now let us assume that Pn...

Homework Statement lim (3/n)^(2n) n→ ∞Homework Equations L'hopital's rule: lim F(a)/G(a) is indeterminate form, then the limit can be written as lim F'(a)/G'(a) x → a x→ a The...

Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...

Oops, the original problem read (1 - z) / 7, NOT (1 - z) / 3. My mistake!

Homework Statement Find the equation that contains the lines: 2x + 3y + 4z = 6, x - 2y + z = 3 and (2x - 1)/22 = (y + 2)/2 = (1 - z)/3 Homework Equations A plane (in point normal form) is defined by a point on the plane and a vector normal to it. In general, the form of A(x -...