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Express (x²+4x+13) / (x+2)²(x-1) as partial fractions. (x²+4x+13) / (x+2)²(x-1) = a/(x+2) +b/(x+2)² +c/(x-1) where a, b and c are constants to be fou...

First we can write d²y/dx² as (d/dx)(dy/dx). Now we need to find dy/dx. This can be further written as (dy/dt)(dt/dx). These derivatives can be obtained from the given parametric equ...

In the exam you will be given a fraction with polynomial numerator and denominator, the denominator will either be factored or factorable. Firstly, you need to factorize the denominator. Then to write as ...

The trick to solving this is to use the trig identity sin(a+b) = sin(a)cos(b) + sin(b)cos(a) From the identity above, we can write rewrite Rsin(x+c) as follows: Rsin(x+c)...

This can be done 'by parts' or by expanding. In this case it would be easier to expand as it is possible to deal with terms individually here.
This becomes: 10xx^1/2 - 10x2
...