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Using a Taylor's series or otherwise; derive Euler's Formula

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(θ) ...
MH
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Politics and prejudice, rather than reasoned argument, are the dominant forces in the Pro Milone.’ To what extent do you agree with this judgement?

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 Latin...
JR
Answered by James R. • Latin tutor
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Solve 3x^2 - 5 = 43

First, we want all the terms with X on one side, so let's +5 to both sides.3x 2 = 48Let's simplify, so we get x 2 on its own.48÷ 3=16x 2 = 16Now, we need x 'unsquared', so we will square root it. √16=4
NM
Answered by Naomi M. • Maths tutor
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Solve 2x^2 = 162

First simplify the equation! This means making the side with your Xs on easier to read.162÷2=81Now we have x 2 = 81 √81=9(Remember 9x9=81.)
NM
Answered by Naomi M. • Maths tutor
5982 Views

Describe the requirements, process and applications for Polymerase Chain Reaction (PCR)

Requirements· Original DNA sample (to be amplified)· dNTPS (4 DNA nucleotide bases)· Thermal cycler (reaction vessel)· Buffer solution (to maintain stable pH)· Taq Polymerase· DNA primers (forward and revers...
VL
Answered by Verity L. • Biology tutor
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