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Suppose you have an equation: (2x+3)/(x-4) - (2x-8)/(2x+1) = 1 and you want to solve for x. Remember that you can only add fractions if they share a common denominator. Also that you can multiply the numerat...

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...

Ah yes, the question which haunted my years of study, particularly during GCSE and A Levels. At this stage, many exams are ‘open book’ - that is, you can take either a blank or highlighted copy of the text i...