Recent content by raphile

Many thanks for the help. Sorry for the late reply - I'm still working on the problem and trying things out. At least now I'm convinced that the condition that f_i(x)/g_i(x) is monotonically increasing for all i=1,2,...,n is not sufficient for the overall ratio to be increasing, which I wasn't...

Hi everyone. In a proof I'm working on, I have a ratio of two sums of functions in the following form: \frac{f_1(x)+f_2(x)+...f_n(x)}{g_1(x)+g_2(x)+...+g_n(x)} I want to prove this ratio is monotonically increasing in x. All of the functions f_i(x) and g_i(x) are positive and also...

Homework Statement Assume that f is a monotone increasing function defined on \mathbb{R} and that for some x_0\in \mathbb{R} the left and right limit coincide. Can you prove that f is continuous at x_0? Either give a complete proof or a counterexample. Homework Equations The...

Thanks for the help and examples!

Hi, I have a small question about this. Using the chain rule, I know that a composition of differentiable functions is differentiable. But is it also true that if a composition of functions is differentiable, then all the functions in the composition must be differentiable? For example, if...

Ok, that's great, thanks!

Hi, The title of the thread doesn't adequately describe the question I want to ask, so here it is: Suppose we have two infinite series, \sum_{n=1}^{\infty}a_n and \sum_{n=1}^{\infty}b_n, both of which are convergent. Also suppose a_n \leq b_n for all n, and a_n < b_n for at least one n...

Thanks a lot!

Hello, I am interested in applying to graduate schools in the US. I understand that I need to take the GRE exam, but I don't know of any test centres in the UK which will allow me to take it. It seems difficult to find this information online. I live in Cardiff so somewhere not too far...

Homework Statement Find the Fourier series for the function f(x) = 1/cos(x) on the segment [-pi/4, pi/4]. Homework Equations A Fourier series for a function f(x) with period 2L has the form: (a0/2) + SUM(n=0 to infinity) [ an*cos((n*pi*x)/L) + bn*sin((n*pi*x)/L) ], where...

But then I would have to integrate (1- x2)n-1dx, and I don't know how to do that when n is unknown. Am I missing something? I tried to integrate it using MAPLE, and it gave me something useless to do with the hypergeometric function.

Homework Statement Let In = \int^{1}_{-1} (1-x^{2})^{n} dx. Use integration by parts to show that In = (\frac{2n}{2n+1}) In-1 for n \geq1. (The integral above is supposed to be between the limits -1 and 1... sorry I couldn't figure out how to make the limits appear...

Homework Statement Evaluate the partial derivatives ∂f/∂x and ∂f/∂y at the origin (0,0), where: f(x,y) = ((xy)^3/2)/(x^2 + y^2) if (x,y) ≠ (0,0); and f(0,0) = 0. Homework Equations ∂f/∂x(x0,y0) = lim(h->0) [(f(x0+h, y0) - f(x0, y0)) / h] ∂f/∂y(x0,y0) = lim(h->0)...

Homework Statement A minibus of mass 1.6 tonnes is rounding a flat bend of constant radius 25m at a steady speed of 72km/h. Find the centripetal force acting on the vehicle. What is the minimum co-efficient of sideways friction between the tyres and the road for this motion to take place...

But in the part of my post that you quoted, I'm not using s at all. I'm just taking the acceleration that I found in the 1st part, (1/2)k^2, and calling it dv/dt, and then solving that to give v in terms of t. Is it not right to say v and t are proportional?