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A general function f(x) has the property f(-x)=-f(x). State a trigonometric function with this property and explain using the Maclaurin series expansion for this function why this property holds. Write down the integral in the limits -q to q of f(x) wrt x

Note that this property is the definition of an odd function, or draw a sketch of what this looks like in general about the horizontal axis. E.g. f(x)=sin(x) which has the expansion f(x)=x-((x^3)/3!)+((x^...

JH
Answered by James H. Maths tutor
4091 Views

What happens to the pressure inside a gas-filled ball when the temperature is increased? Explain your answer, stating the assumption made.

From definition of pressure have P=F/A (in reality for a ball we are talking about infinitesimal areas, but the general definition is sufficient at this level). Assume that the area of the surface under c...

JH
Answered by James H. Physics tutor
2176 Views

How do I know if an enthalpy change should be positive or negative?

A negative enthalpy change represents an exothermic change where energy is released from the reaction, a positive enthalpy change represents an endothermic reaction where energy is taken in from the surro...

AS
Answered by Alex S. Chemistry tutor
87926 Views

Examine the importance of spectacle in the Tempest with comparative reference to Dr Faustus

The play The Tempest is itself a giant spectacle; from the grand illusionary storm which opens the performance and continuing throughout, all in the name of achieving Prospero’s engineered plot. The use o...

CJ
Answered by Caitlin J. English tutor
11459 Views

Describe the process of natural selection

There is genetic diversity within the population. Random mutation can occur, forming new alleles of a gene. Though many mutations are harmful, in certain environments the new allele may benefit its posses...

JJ
Answered by Jewel J. Biology tutor
9625 Views

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