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Maths
A Level

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+...

MO
Answered by Mojowo O. Maths tutor
9961 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...

OL
Answered by Oliver L. Maths tutor
9332 Views

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(GH)−log(1/M)−2logR             using law of addition
logF=log(G
HM)−2logR                      ...

AR
Answered by Ambrose R. Maths tutor
6556 Views

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 = xn then dy/dx = nxn-1

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PW
Answered by Percy W. Maths tutor
6339 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=r2. On...

BA
Answered by Bea A. Maths tutor
6999 Views

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