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Simplify (3x^2 + x -2)/(x^2 - 1)

First notice that no simplifications can be made to the problem without changing the form. We start by factorising the numerator. The highest power of x in this question is 2, therefore we know that it ha...

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Answered by Arjun A. Maths tutor
4098 Views

Integrate x^3 * lnx

I would start by asking the student the different forms of integration we know (e.g. substitution, parts).I would then ask the student whether parts or substitution gives the easiest method.If the student...

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Answered by Arjun A. Maths tutor
2797 Views

Find the stationary points and their nature of the curve y = 3x^3 - 7x + 2x^-1

To start, we need to know that the gradient of the curve at the stationary points is 0 and that when the second derivative is less than 0, there is a maximum and when the derivative is greater than 0, the...

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Answered by Arjun A. Maths tutor
4204 Views

Determine the equation of the line which is perpendicular to y = 2x + 9 and crosses through the point (1,2)

When multiplied together the gradients of perpendicular lines should give the answer - 1So: x1x2 = -1x1 = 2 x2 = -1/2It crosses through the point (1,2)y = ax+ b...

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Answered by Aneisha D. Maths tutor
2788 Views

A linear sequence starts: a+2b, a+6b, a+10b, ..., ... The 2nd term has a value of 8. The 5th term has a value of 44. Work out the values of a and b.

We know the values for the 2nd and 5th terms and already have the 2nd term as an equation but not the 5th. Therefore, we need to start by working out what exactly the 5th term is in terms of a and b. From...

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Answered by Molly T. Maths tutor
2693 Views

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