Recent content by PedroB

Homework Statement Find the derivative of the function f(x)=cos(√x) by first principles Homework Equations f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h The Attempt at a Solution Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've...

Homework Statement I'm almost embarrassed to post this, but insofar none of my searches online have yielded any results. My question is simply, given a parallel plate capacitor (for the purpose of simplicity let's assume that there are no edge effects) whose constituent plates have charge +aQ...

Homework Statement I'm currently tackling parts (a) and (b) of section ii) decribed here:http://puu.sh/31KIZ.png Homework Equations V=(q/4∏ε)*(1/r) The Attempt at a Solution From the first section (i) calculating the potential was relatively straight forward since we were only...

Homework Statement What would be the limits for each of the integrals (one with respect to x, one with respect to y) of an area bounded by y=0, y=x and x^2+y^2=1? Homework Equations None that I can fathom The Attempt at a Solution I've rearranged the latter most equation to get...

Homework Statement Show, using complex numbers, that sin(x)+cos(x)=(√2)cos(x-∏/4) Homework Equations cos(x)=(e^(ix)+e^(-ix))/2 sin(x)=(e^(ix)-e^(-ix))/2i e^ix=cos(x)+isin(x) The Attempt at a Solution I was given the hint that sin(x)=Re(-ie^(ix)), but have thus far not been...

My mistake, I apologize, the polar form will therefore be ((√2)^z,(z∏/4)). Is this it then? It seems too simple (from experience of the questions I've been given in the past), but if this is truly expressing the equation in polar coordinate form is there nothing more I can do to it? Would it be...

If I express (1+i)^z by substituting the (1+i) equivalence in polar form I simply get (cos(z∏/4)+isin(z∏/4)). What I don't understand is if by expressing it in polar coordinates they mean for me to actually plot the graph on the complex plane. If this is the case I still do not see how I can get...

Homework Statement Consider the complex function f (z) = (1 + i)^z with z ε ℂ. 1. Express f in polar coordinates. Homework Equations The main derived equations are in the following section, there is no 'special rule' that I (to my knowledge) need to apply here. The Attempt at a...

Ok, so I get q= ∏/2 (which makes sense since tan(∏/2)= ∞), but what does this mean exactly? Are the range of values when x + iy = ∏/2? Surely this simply leads to x = ∏/2 which is evidently not a 'range' of values. This is the simpler of problems that I need to do, though it's the one that's...

Homework Statement Let tan(q) with q ε ℂ be defined as the natural extension of tan(x) for real values Find all the values in the complex plane for which |tan(q)| = ∞ Homework Equations Expressing tan(q) as complex exponentials: (e^iq - e^(-iq))/i(e^iq + e^(-iq)) The Attempt...

Homework Statement 1. A vector u is given by u = λa + μb, where λ, μ are elements of ℝ. Calculate axu and bxu and show that: [(b χ u).n]/[(b χ a).n] = λ and [(a χ u).n]/[(a χ b).n] = μ (In any circumstance when I have omitted the underlining it is for convenience purposes, a, b...

Yes, it is something along those lines. If you don't mind (I really appreciate the effort, don't want to seem disrespectful) can you please post the formula (or link to said formula)? Also, from what I gathered from my research, solid angles are and I quote "two-dimensional angle in...

Homework Statement Simply put, I am conducting an investigation that determines the "optimum" wavelength of light for solar panels (ie the wavelength which produces the highest conversion efficiency). To do this however, I need to know the energy input of incident light on a particular...

In metals, electrons flow through the 'layers' of metal cations when a current is made to flow through them. As temperature increases, these ions vibrate more vigorously, thus interfering with the electron's movement (to use an analogy, it would be similar to a sideways collision with a moving...

I had considered this, but the fundamental concepts are quite disparate. Whilst in metals increased temperature causes individual particles to vibrate more (thus interfering with the electrons' paths, which leads to a decrease in conductivity), in electrolytes, there is no 'interfering agent'...