## Answers by Aaron S.

No, here is one way you can think of it:   Remember the rule that:   xm/xn = xm-n   (if x≠0)   So if m = n, this says:   xm/xm = x0   But clearly xm/xm = 1, so we must have that     x0 = 1 as well.   Be...

As a quick check, if we are to have any hope of factoring a quadratic equation (of the form  ax2+bx+c = 0) into linear factors with rational coeffecients we must have that the discriminant of the quadratic equation (which is defined to be:  b2 - 4ac) is a perfect...

I'm not sure from what approach you are being asked to solve this question (e.g. linear algebra, precalculus, etc.), but I'll assume it's something along the lines of precalculus.    Since we have only 1 equation and 4 unknowns, we simply solve for any 1 variable, let's say a:   a...

This is actually a lot more intuitive than it seems. For 1-dimensional derivatives, we have that the best linear approximation of f(x) near x=a is:   f(x) ≈ f(a) + f'(a) * (x-a)   We have the same thing for higher dimensions:   R(x) ≈ R(a) +...

I'm a little unsure as to what you are asking about. Are you asking why/how we get this differential equation? If that is your question, I'll try to help.    If we use Kirchhoff's voltage law, we have that:   sum of potential differences = 0.    If we assign,...