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The first step is to prove that the result is true for n=1.The second step is to assume that the result is true for n=k where k is any positive integer.The third step is to prove that the results is true ...

At the minimum point, the gradient will be zero, so we differentiate the equation, giving us dy/dx = 3e^3x - 12e^2x. If the gradient is zero at the minimum point, we can set dy/dx = 0,...

1. First we need to make sure we have a nicely labelled triangle, identifying which sides are the adjacent, opposite and hypotenuse. 2) Once these are labelled we will can work out which trig function ...

The first step here is to identify what to do. Differentiating the equation y = 2x^2 + 7 will result in dy/dx = 4x. Given that you know that x = 3, you can substitute x = 3 into 4x which gives you 4(3) = ...

First split up the fraction into partial fractions as this is more easily integrated. It can be seen that the denominator has factors y and (3y+2), therefore we can say the original fraction is equal to p...