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Integral of 1/(x^3 + 2x^2 -x - 2)

Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+1) using integral 1/x = ln(x...
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Answered by Mojowo O. • Maths tutor
10056 Views

A curve has the equation 2x^2 + xy - y^2 +18 = 0. (1) Find the coordinates of the points where the tangent to the curve is parallel to the x-axis.

Firstly notice that the coordinates of the points where the tangent to the curve is parallel to the x-axis are precisely the points where the rate of change of y with respect to x is not changing. That is, w...
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Answered by Oliver L. • Maths tutor
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Rewrite ... logF=logG+logH−log(1/M)−2*logR ... in the form F=... using laws of logarithms

logF=logG+logH−log(1/M)−2*logR Simplify RHS using law of logarithms, logF=log(G H)−log(1/M)−2logR using law of addition logF=log(G H M)−2 logR using law of subtraction logF=log((G H M)/R^2)) using law of pow...
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Answered by Ambrose R. • Maths tutor
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Find the stationary point on the line of y = 6x - x^2 and state whether this point is a maximum or a minimum

This question requires differentiating the equation to find where its gradient is equal to zero. Differentation is done via a simple equation --> if y = x n then dy/dx = nx n-1 Therefore if y = 6x - x 2 ,...
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Answered by Percy W. • Maths tutor
6418 Views

A circle is given by the equation x^2+y^2-20x-24y+195=0. Draw this circle.

In order to answer this question, we must transform this equation for a circle into the general form of an equation of a circle; namely something like (x-a) 2 +(y-b) 2 =r 2 . Once we have done this, we know ...
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Answered by Bea A. • Maths tutor
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