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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
3956 Views

Translate the following sentence: My friends and I like to help old people when we can. We have no time now because we get a lot of homework.

Things that they are testing here: 'to help' = helfen + DATIVE; 'because' = weil (sends main verb to the END); general adjectival endings and plurals ANSWER(S): Meine Freunde und ich helfen gern ( like to ca...
ZG
Answered by Zac G. • German tutor
2122 Views

Solve the simultaneous equations: 3x-y=1, x^2+y^2=5

x=1, y=2 x=-2/5, y=-11/5
CW
Answered by Chloe W. • Maths tutor
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How have ideas about atomic structure changed through history?

The Greeks were the first to think of atoms, Democritus defined an atom as the smallest indivisible piece of matter using the idea that if you continue to cut a material in half, you must eventually reach a ...
SW
Answered by Scott W. • Chemistry tutor
3844 Views

Explain how an increase in the level of taxation can affect the level of aggregate demand

Aggregate demand is the sum of consumption, investment, government spending and net exports.Consumption can change for various reasons such as changes in income, taxes, expectations about future income, and ...
JS
Answered by Jose S. • Economics tutor
8399 Views