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A function, y = f(x), with y on the vertical axis and x on the horizontal axis, can be transformed by 3 different ways: It can be stretched (or shrunk)If y = f(ax), the function is stretc...

x_n = ar^(n-1)(1) x₂ = 750 = ar¹(2) x₅ = -6 = ar⁴divide second equation by first-6/750 = r³r³ = -0.008r= -0.2Insert in...

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...