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Let f(x)=xln(x)-x. Find f'(x). Hence or otherwise, evaluate the integral of ln(x^3) between 1 and e.

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x). Now note that ln(x^3)=3ln(x) using propertie...
MJ
Answered by Matthew J. • Maths tutor
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Describe the stages of mitosis?

First the chromosomes condense and the centrioles form and spindles project from them. This is the prophase. The nuclear membrane breaks down and the spindle attaches to the chromosome. Then the chromosomes ...
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Answered by Harry D. • Biology tutor
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Explain why the use of petrol and diesel cars may be a source of market failure.

Use of petrol and diesel cars causes over-pollution to the environment, which is an externality in the economy. The overconsumption of petrol and diesel cars results in more pollution and emissions than is s...
SM
Answered by Seb M. • Economics tutor
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When do you use the subjunctive mood?

There are three things that lead us to use the subjunctive mood, instead of the normal indicative. These are what we call triggers. 1) There must be a change of person in the sentence.2) There must be a rela...
KT
Answered by Kane T. • Spanish tutor
2051 Views

Cells go through a series of stages in order to replicate themselves, called mitosis. Briefly describe each stage of mitosis. (8)

1 mark for each name1 mark for each explanation Prophase - DNA condenses into chromosomesMetaphase - Chromosomes line up along equator of cellAnaphase - Sister chromatids pulled apart to form two identical d...
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Answered by Charlie H. • Biology tutor
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