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First, we must differentiate the function. To do this we must let the contents of the bracket be equal to 'u'. We now can produce two equations, one by subbing in 'u' into the function f(x) to give us u^5...

You fill the 5-litres jug, and pour it into the 3-litres jug until it's full (now you have 2 litres in the 5-litres jug). Then, you pour out the 3-litres jug completely. Now, you pour the 2 litres from th...

Let n be an odd integer. This means that n is 1 more than an even integer. By definition, even integers are multiples of 2 so all even integers can be written in the form 2m where m is an integer. Therefo...

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...

Let's do an example. Sketch: y=x^3 - 2x^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 ...