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...
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...
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...
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...