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Evaluate the following integral: (x^4 - x^2 +2)/(x^2(x-1)) dx

This type of question appears over-complicated with limited options, but one must not fear! At first, the numerator seems to be of a higher degree than the denominator (x^4 compared to x^2), but from the fir...
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Answered by Nicholas H. • Maths tutor
6747 Views

Differentiate the function f(x) = 3x^2/sin(2x)

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6x sin(2x). uv' = 6x^2 cos(2x), v^2 = 4cos^2(2x) Therefore the differential is [...
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Answered by Kilian S. • Maths tutor
6587 Views

Comment on whether an increase in saving will reduce inflation

If there is an increase in saving, then assuming that income stays exactly the same, this will mean that there is a fall in spending as we are saving a higher proportion of our income - or in other words our...
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Answered by James K. • Economics tutor
6924 Views

Solve algebraically the simultaneous equations: x^2+y^2 = 25 and y-3x=13

To answer this question, we need to make y the subject of the second equation. We can do this through simple rearrangement: y-3x=13 so y=13+3x Now that we have y on its own, this means we can substitute for ...
JK
Answered by James K. • Maths tutor
8903 Views

Differentiate the function f(x)=2xsin3x

Use the product rule: u'v + uv' u = 2x V= sin3x u'= 2 v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x
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Answered by Thomas W. • Maths tutor
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