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Suppose you have 2 functions: f(x) = 3x 2 , g(x) = log 3 (x). These are arbitrary, any functions would work. Evaluate f(g(x)): let y = log 3 (x) ( = g(x) ), then f(g(x)) = f(y) = 3y 2 = 3[log 3 (x)] 2 . The ...

The most important thing to remember when differentiating implicitly is that y is a function of x. Rewriting y as y(x) often makes it much clearer. For example, evaluate d/dx (y 2 ): using the aforementioned...

First, we need to find the value of t when x = 6p°C. We are told that after t minutes the temperature, x, will be 60°C; so we can insert 60 into the equation for x: 60 = 15 + 70e^(-t/40) Secondly, we can rea...

The cardiac cycle is the series of events that leads to blood being pumped to the lungs and around the body. The cycle begins with the SAN (sino-atrial node). This is the hearts 'pacemaker'. It sends out a n...

This fraction can’t be integrated easily, but if we split it using partial fractions, these will be easier to integrate. To do this, we need to factoise the denominator, as this will follow the method of par...