Ok I've substituted x = at, now I get
\int_{-\infty}^{\infty}\phi(\frac{x}{a})\delta(x)d\frac{x}{a} = \frac{1}{a}\int_{-\infty}^{\infty}\phi(\frac{x}{a})\delta(x)dx = \frac{1}{a}\phi(\frac{0}{a}) = \frac{1}{a}\phi(0)
I don't quite see how I'm allowed to take the 1/a out of the d/dx...
Homework Statement
Prove that \delta(at)=\frac{1}{abs(a)}\delta(t)
Hint: Show that \int\phi(t)\delta(at)dt=\frac{1}{abs(a)}\phi(0)
(the limits of integration are from -inf to +inf btw, I couldn't find how to put them in..)
Homework Equations
The Attempt at a Solution
Ok. I...
But the function is w.r.t x, so my first thought was just to drop the x off. But that's wrong...
I don't get it, what's f and what's g?
Thanks for somewhere to start though
We were given in a previous question,
s_{N}(x) = \frac{4}{\pi}\sum_{n=0}^{N-1}\frac{sin(2n+1)x}{2n+1}
Homework Statement
Show that
s'_{N}(x) = \frac{2sin(2Nx)}{\pi sinx}, x \neq l\pi
and
s'_{N}(x) = \frac{4N}{\pi}(-1)^l, x = l\pi
where l is any integer.
The Attempt at a Solution...
Homework Statement
Evaluate the following triple integral
I = \int\int\int_{R}x dv
in Cartesian coordinates where R is the finite region bounded by the surfaces z=0, y=x^3, y=8, z=x. Sketch the region R. Here dV is the element of volume.
Homework Equations
The Attempt at a...
Homework Statement
Not really a problem, but we're learning about source-free RL circuits and the instructor was deriving the current w.r.t time. I've actually seen this derived a few times but one thing has always bothered me.
Looking at this picture recreated from the text...
Thanks, that makes sense. Another question though, looking at source three, it looks to me like there are two voltages over it, 2V from the very left hand side and 10V from the voltage source. Why do you pick 10V over the 2V?
As far as I understood everything in parallel has the same voltage...
Thanks mplayer you're great, I'm just skimming over what you've written but got confused by the above quote, we've been taught in class that the PSC convention is current entering the positive terminal, not the other way around...?
Homework Statement
Determine which of the five sources in Fig. (attached) are being charged (absorbing positive power), and show that the algebraic sum of the five absorbed power values is zero.
I've labelled how I'm referring to the sources in red...
Experimenting with building a wind turbine and I'm trying to find a suitable motor.
I got this induction motor out of a washing machine and have hooked it up through a bridge rectifier and a smoothing capacitor.
Spinning the motor shaft by hand (a crude way of modeling how fast the wind...
AC motor from washing machine, has 11 wires from it. Aside from Earth I have no idea what they are however I have observed:
If the white+blue OR the red+orange wires are bought into contact then the shaft becomes hard to turn AND I can get a few small sparks by spinning the shaft and quickly...
Homework Statement
A block having mass m and charge +Q is connected to an insulating spring having constant k. The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric field of magnitude E as shown in the diagram. If the block is released...
I have the correct answer just the wrong direction
Homework Statement
A uniformly charged insulating rod of length 14.0cm is bent into the shape of a semicircle as shown in figure XXX. The rod has a total charge of 7.5 micro C. Find the magnitude and direction of the electric field at P...
Coming out with "clean" values for arccos, arcsine and arctan
Homework Statement
Not so much a homework problem just something that bugs me and it's taken until first year Uni math before I asked it.
In the text or in lectures when taking the arccos of say, 1/root2, the lecturer won't write...
Homework Statement
Evaluate lim (1+a/x)^x
(that's limit as x tends to +infinity, sorry don't know how to latex that)
Homework Equations
The Attempt at a Solution
Stumped. Having that x exponent has my confused. As x tends to infinity I know what's inside the brackets will tend to one, but the...