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First we must consider for which values of x the equation: 3/(x+3) = (x-4)/x is undefined. In this case, x=-3, and x=0. 

Now we must consider each of the cases, x<-3, -3<x<0, 0&l...

To find power we are going to need the equation:

P = F v 

Where P is power, F is force and v is velocity

Since the car is travelling at a constant speed up the...

Divide through by x so:      (dy/dx) +2(y/x) = 4x

Now multiply through by the intergrating factor:  e^(| (2/x) dx) = e^(2.ln(x)) = x^2

so you get:     (x^2)(dy/dx) + 2xy = 4...

In complex number ( especially for any real number) x and integer n it holds that

(cos(x) + i(sinx))^n = cos(nx) + isin(nx) where i is the imaginary unit repres...

At first glance, this may look like an inverse trig integral but as the top contains an x term, we must use a different method.

First, rewrite the top in two parts, one that is a multiple...