Recent content by tedwillis

First, I've had to find the Fourier series of F(t) = |sin(t)|, which I've calculated as f(t) = \frac{2}{\pi} + \sum_{n=1}^{\infty}\frac{4cos(2nt)}{\pi-4\pi n^2} I'm pretty sure that's right, but now I need to evaluate the sum using the above Fourier series...

Homework Statement Have a few limits that I'm stuck on: a) lim n->infinity (n(n+1)^(n+1))/(n+2)^(n+2)) b) lim n->infinity (n^n/(n+3)^(n+1)) c) lim n->infinity n^(-1)^n I've tried my best to understand what to do solve these, but can't get it. We've been given answers to standard...

Woops. That was a typo actually. It should say my''(t)=mg-k(s+y(t))-by'(t) instead, and this is the path that the following calculations take. In this sense, I am saying that the restoring force of the spring’s tension (T) is equal to the spring constant*(contraction (or extension)+y(t)...

Hi all, I was wondering is you could help me with this springs question. We've only done springs hanging from a fixed support above being stretched, but now I've got a question where the spirng is being compressed. Homework Statement So, here's some basic info about the question...

So I guess this is what you mean by standard form: $$9t^3+900t^2+30000t-1000000=0$$

Oh sorry, I forgot to mention the intial vlaue is x(0)=0

Here's some more info on the problem that may help: x(t) is the amount of an element in a container The original d.e: $$dx/dt+6x/(100+3t)=3$$ 100+3t=v, the total volume of liquid in a container over time. The max of this is 300. Solving the d.e gives...

Sorry, wrote the question wrong: 3t+100=4((9t^3+900t^2+30000t)/(3t+100)^2)

Hi, I need to solve this equation that stems from a differential equation, though that isn't really important. Here's the equation that needs to be solved for t: 3t+100=4((9t^3+900t^2+30000t)/(3t+100)… I've tried myself and always seem to hit a dead end. Using a calculator, I know the...

Thanks for your help.

Woops. So a=√27/√b? So your saying the domain of A is 2<=a<=27/a^2? Can you explain why to solve 27/a^2=2? Anyway, A(2)=62mm^2 So, for the second part, should I solve 27/a^2=2 for a, then sub this value the Area equation? The above equation solved for a=√27/√2. A(√27/√2)=12√6 + 27 which...

Thanks for the response. So I've done that. b=27/a^2 and a=27/b The equation for the total surface area in terms of a and b is: Area = 2a^2 + 4ab subbing b=27/a^2 gives: Area = 2a^2 + 108/a dA/da = 4a - 108/a^2 The area equation is a weird graph where the function is always...

but I have a headache. Here's the question: A laundry powder company wishes to produce a 27mm^3 washing powder capsule in the shape of a rectangular box. Due to production rescrictions, the width and the depth of the capsule must be equal lengths, and all dimensions of the capsule must be equal...