Recent content by Thomas_

I need to show that \sum_{i=0}^n i^k=\Theta(n^{k+1}) Or equivalently \lim_{n\to\infty}\frac{\sum_{i=0}^n i^k}{n^{k+1}}=CI simply don't know what to do with the sum here. I know that I can rewrite or expand it, but that doesn't seem to help me. Any suggestions? Thank you!

Look at the examples on the website I posted. It's basically one line of code, you don't need an extra method for that.

You can do this in one line of code with regular expressions. http://www.regular-expressions.info/ http://www.regular-expressions.info/java.html

Homework Statement Let : f(x,y) = \frac{xy(x^2 - y^2)}{(x^2 + y^2)^2} if (x,y) \neq (0,0) f(x,y) = 0 if (x,y) = (0,0) a) Find f_{xx}(0,0) b) Find f_{xy}(0,0) c) Find f_{yx}(0,0) Homework Equations None The Attempt at a Solution I'm not sure how to deal with the piecewise...

Thank you very much for your answer. That would mean that r''(t) is the 0-vector. Which means that there is no acceleration, no change of direction, motion should be straight. However, my professor told me that this is not formal enough. I tried to arrive at a similar conclusion by using ||a...

Homework Statement Proof that, if a particle moves along a space curve with curvature 0, then its motion is a along a line.Homework Equations K=\frac{||r'(t)\times r''(t)||}{(||r'(t)||)^3} (curvature of a space curve)The Attempt at a Solution Assume the curve is smooth, so r'(t) cannot be the...

Ups sorry, the differentiation error was just a typing mistake ;) When the velocity is maximum, the acceleration at that point should be 0? So it can't be the same t. But how does that help me?

Homework Statement A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.381m. The maximum transverse acceleration of a point at the middle of the segment is 8200 m/s^2 and the max. transverse velocity...

Well, they give me a picture with the arc starting from the positive x axis, going through an angle alpha which is counterclockwise from the positive x-axis. That's what is confusing me... Also, shouldn't there be two components to the elctric field? X and y? Regardless of where the arc is...

Homework Statement Determine the field at the center of curvature of an arc of arbitary angle \alpha (\alpha is with the x-axis) Homework Equations E=\frac{kQ}{R^2}\widehat{r} S=R\alpha \lambda=\frac{Q}{S} The Attempt at a Solution I divide the arc into small pieces ds...

I can't follow you on this one. Yes, I know that a_{tan}=r\alpha for a rigid body, but I don't see any angular/linear accelerations in the equation we would have to "convert". My goal is to get g=(\frac{2\pi}{T})^2L

Hm, thank you. I used \sum\tau = I\alpha) and came up with: \sum\tau = -k\frac{L}{2}sin(\theta)(\frac{L}{2}cos(\theta)) = -k\frac{L^2}{4}\theta => I\alpha + k\frac{L^2}{4}\theta = I\frac{d^2\theta}{dt^2} + k\frac{L^2}{4}\theta = 0 That should be SHM. However, how do they get to...

Hello, I have problems solving the following two problems: 1)You measure the period of a physical pendulum about one pivot point to be T. Then you find another pivot point on the opposite side of the center of mass that gives the same period. The two points are separated by a distance L. Use...

Sorry, I do not quite understand what you mean or how this helps me. Could you elaborate on that? Also, I am interested in why the test I am using does not work out like it should or if I made an algebra mistake somewhere along the way.

Hello, I have to prove conv/div. for the following series: \sum\frac{(2n)!}{n^n} I use the "ratio-test" and get the following: \lim_{n\to\infty} \frac{a_{n+1}}{a_{n}} = \lim_{n\to\infty} \frac{(2n+2)!}{(2n)!} \frac{n^n}{(n+1)^{n+1}} = \lim_{n\to\infty} \frac{(2n+2)(2n+1)}{(n+1)}...