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This question requires selecting the correct double angle formulae.
cos(2x)=2cos^2(x)-1 is rearranged to 1/2(cos(2x)+1)
this can now be integrated with the students knowledge of standard integra...

Because there are two functions that are enclosed in brackets, you should realise that you need to differentiate by parts. You can expand out and differentiate through, but because of the x^1/2 it can get...

This is a minimisation problem, but it's slightly tricky to see what it is we're minimising. Seeing as it's a that's varying, we are going to have to differentiate with respect to a at some point. We're g...

First make left =0x²+y²-6x+4y+4=0Second put same terms together(x²-6x)+(y²+4y)+4=0Complete the Square (do a square (X+b)² that gives you you x^{2 ...}

The most simple way to find the gradient of a quadratic curve at a point is to differentiate. Through differentiation a function for the gradient at each value of x can be found. 'y' must be isolated on o...