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Use the Taylor series expansion for the following three functions: f(θ) = e^(iθ), g(θ) = cos(θ) and h(θ) = sin(θ). We should find that f(θ) = e^(iθ) = 1 + iθ - (θ^2/2!) - i(θ^3/3!) + ... = Sum(θ^n/n!), g(...

n.b Whilst this answer addresses Cicero’s ‘Pro Milone’, the approach demonstrated here may be successfully applied to any text, verse or prose, that might be set for the 20 mark ‘essay question’ of the La...

First, we want all the terms with X on one side, so let's +5 to both sides.3x² = 48Let's simplify, so we get x² on its own.48÷ 3=16x² = 16Now, we need x 'unsquared', so we...

First simplify the equation! This means making the side with your Xs on easier to read.162÷2=81Now we have x² = 81 √81=9(Remember 9x9=81.)

Requirements·            Original DNA sample (to be amplified)·            dNTPS (4 DNA nucleotide bases)·            Thermal cycler (reaction vessel)·            Buffer solution (to maintain stable pH)· ...