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QUESTION: Given the equation x³-12x²+ax-48 = 0 has roots p, 2p and 3p, find p and a. Roots mean x = p, x = 2p and x = 3p hence (x-p), (x-2p) and (x-3p) are factors of the equation. E...

Will be easier to explain with whiteboard!a) Let y = arcsin x. sin y = x cos y dy/dx = 1 dy/dx = 1/(cos y) dy/dx = 1/(√ (1 - sin²y)) dy/dx = 1/(√( 1 - x²)) as required.b) 4 - 2x - x<...

We can write this sum S as Re(e^ix+e^2ix+...+e^nix), we now have a finite geometric series, which we know the formula for.Have, S = Re( e^ix(1-e^inx)/(1-e^ix)) - Now factoring numerator and denominator to...

Improper integrals can take many forms. The first step when dealing with a potentially improper integral is to test the limits of the integral i.e. a and b. If these are at infinity/negative infinity, or ...

For the first part this is a standard polynomial integral whereby we can follow the power rule for anti-differentiation. In part ii), if we look at the question we see that we're trying to get I(n-1) in o...