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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...
NH
Answered by Nicholas H. • Maths tutor
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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
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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...
JK
Answered by James K. • Economics tutor
7017 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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Describe and explain Anselm's Ontological Argument.

The Ontological Argument is one of five classical arguments for the existence of God, using a prior logic (knowledge without experience). It was formulated primarily by St Anselm (1033-1109), defining God as...
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