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dy/dx = 1 - 12x² + 2x^(-5)

First of all determine the range of the function by looking at its denominator. The function is defined at each point except x=-2 Now to find the zeros o...

So this initially looks like a tricky question- especially the way it is written in the form of x as a function of y, ( x(y) ), rather than what we normally see y as a function of x, ( y(x) ).The first th...

To answer this we need to consider a circle of radius r centred at the origin, drawn in the x,y plane. We'll draw a right-angled triangle such that the hypotenuse is the radius, and say that the point whe...

The question asks for integration by parts. Therefore we need to differentiate one variable and integrate the other. First we need to decide which variable is going to be which. Algebra should always be d...