Search over 10,000 free study notes

Firstly, the equation should be rearranged to get all the non-zero terms onto one side, with the simplest way of doing this being subtracting 12 from both sides, giving the equation x 2 - x - 12 < 0. Then...

First you should express this in the correct format using the integral sign. We need to find the integral with respect to x so include dx in the equation before integrating. To integrate we add one to the po...

Let's do an example. Sketch: y=x^3 - 2 x^2 - x + 2. First we need to find out where the curve crosses the x and y axes. Look at the x axis first. We factorise the expression if we can. The best method to fac...

To prove n 3 -n is a multiple of 3 we rely on a few simple tricks. The first is to factorise the expression.n 3 -n = n(n 2 -1)n(n 2 -1) = (n-1)(n)(n+1)The next trick is to realise that the series of numbers ...

Now remember that for differentiating polynomials the power is times by the coefficient and the power is reduced by one. This would mean that the answer now becomes: 2x + 2