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This problem tests two key sub-topics in calculus, kinematics and the chain rule. Firstly, you must realise that the derivative of a velocity function will give you the acceleration function. So by findin...

To find the points at which an equation intersects the x-axis, we first need to factorise the equation to be able to find the solutions. To do this, we consider the general form of a quadratic equation a...

First of all instead ,we'll define the chain rule , thus y can be rewritten as y = f (g(x)) , where f(x) = exp (x) and g(x) = cos^2(x) + sin^2(x). Therefore let y = f(u) , dy/dx = dy/du * du/dx , which ...

To find the x coordinate of point P, we simply substitute in the value of y at P into the equation of the curve and solve for x = 4pi^2. (ii) To start, we can differentiate x with respect to y, by using t...

First, clearly write the two equations above one another, and label them (1) and (2). Rearrange the linear equation (the one with no squared variables) to make y the subject of the equation. You should ge...