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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 ...
To prove n3-n is a multiple of 3 we rely on a few simple tricks. The first is to factorise the expression.n3-n = n(n2-1)n(n2-1) = (n-1)(n)(n+1)The next trick is...
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