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First, we need to look for a pattern. What are we needing to do to get from one number to the next? As you can see, we are multiplying each number by two to get the next number. 8 multiplied by 2 is 16, a...

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...