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The equation of a circle is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the centre of the circle, and r is the radius. To condense our equation into this form we have to use the technique of completing the sq...

To find the turning points of a curve one must find the values of x which satisfy dy/dx = 0. To further determine what type of turning point this is you need to compute the second derivative with respect ...

To put this equation into partial fractions we need to consider it in the form: (5x + 4)/(x +2)(x - 1) = A/(x + 2) + B/(x - 1) where A and B are numbers we are trying to find. To do this we need to multip...

Here the key is to remember to differentiate with both x and y with respect to x, where the differential of y is dy/dx. Consider the first term, 3x² : This differentiates to 6x. This is done by...

This can be achieved through integrating by parts. The term we wish to differentiate and ultimately eliminate here is the x^2 term. There by applying the formula twice the integration can be accomplished....