Recent content by WilcoRogers

Uhh not if the set has a hole in the middle... then it's not convex.

Well i know the function is convex on that region, intuitively, because of how it looks. I know the definition of a convex line, but I can't show it. I feel, given the nature of this problem, the answer is staring me in the face, but I can't seem to get an algebraic statement that makes sense.

I know that we can say y_1\ge 1/x_1 and y_2\ge 1/x_2, and that we can add those constraints, but they don't get me anywhere. I know that I have to show, somehow that (1-\lambda)P_1 + \lambda P_2 is also in the set. I just don't know how to set up the proof and inequalities, or how that whole...

Homework Statement Using the definition of a convex set, show that the set in R^2 \{(x,y) \in R^2 \colon y \ge 1/x, x\ge 0\} Homework Equations An object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the...

Hello, I am trying to show that: \delta(x) = \lim_{\epsilon \to 0} \frac{\sin(\frac{x}{\epsilon})}{\pi x} Is a viable representation of the dirac delta function. More specifically, it has to satisfy: \int_{-\infty}^{\infty} \delta(x) f(x) dx = f(0) I know that the integral of...

Hello, I am trying to show that: \delta(x) = \lim_{\epsilon \to 0} \frac{\sin(\frac{x}{\epsilon})}{\pi x} Is a viable representation of the dirac delta function. More specifically, it has to satisfy: \int_{-\infty}^{\infty} \delta(x) f(x) dx = f(0) I know that the integral of...

This question uses the Biot-Savart Law: B = \frac{\mu_0 I}{4\pi}\int \frac{d\vec{l} \times \hat{r}}{r^2} In this case, use cylindrical co-ordinates to find your field for the two radii. For the straight parts, the current is parallel to the r-hat vector, and as such the B-field is zero on...

Nobody has any idea?

Homework Statement Suppose that two people are dividing two cakes using the following rules: 1. The first person divides the first cake into two pieces in any fashion. 2. The second person then chooses which of the two cakes they will get to choose the first piece from. 3. The first person...