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Express f(x) = ln(x+1) as an infinite series in ascending powers of x up to the 3rd power of x

Recall that the Maclaurin series for f(x) is f(x) = f(0) + f'(0)x + f''(0)x 2 /2! + ... + f (r) (0)x r /r! + ... Here f(0) = ln(1+0) = ln1 = 0 , f'(x) = 1/(1+x) using the chain rule. f'(0) = 1/1 = 1 , f''(x)...
CP
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The air pressure in the cabin of a passenger plane is modelled by the equation: P(x) = 3cos(x/2) - sin(x/2) where x is the altitude. Express P(x) in the form Rcos(x/2 +z) where z is acute and in degrees and then find the maximum pressure

This is a classic example of a trigonometry problem using the angle addition formulae. Recall that cos(A+B) = cos(A)cos(B) - sin(A)sin(B). Express R(x/2 -z) in similar form: Rcos(x/2 +z) = Rcos(x/2)cos(z) - ...
CP
Answered by Caspar P. • Maths tutor
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Describe the role of a ribosome in the production of a polypeptide.

The ribosome binds to the mRNA and reads the codon codeThe ribosome brings the correct tRNA molecules to each mRNA codon, using complementary base pairing between the mRNA codons and the tRNA anticodonsEach ...
EH
Answered by Elizabeth H. • Biology tutor
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How would our Sun's luminosity change if we increased its temperature 3 times?

The luminosity of our Sun could be derived by the Stefan-Boltzmann, otherwise known as Luminosity law. It says the total energy produced by a unit surface per unit time area (power per unit area) is: (power ...
DG
Answered by Denislav G. • Physics tutor
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“Finances greater decide a woman’s fate than patriarchy.” Discuss this idea in relation to Jane in Jane Eyre.

Being released by Brontë in 1847 and set a few years earlier, the economic impact of the industrial revolution permeates all aspects of society in Jane Eyre. Many women of the time period, like Jane herself,...
OH
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