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Whenever possible it is always a good idea to draw a graph to give a better understanding of what is going on in the question. As we have already been given a point on the tangent, namely A(10,7), it is a...

First, separate the algebraic fraction:(x+7) / ((x-3)(x+1)² = A/(x+3) + B/(x+1) + C/(x+1)² Multiply both sides by (x-3)(x+1)²: (x+7) = A(x+1)²+ B(x+1)(x+3) + C(...

First, the surds need to be simplified. Surds can be simplified by finding the highest square number that is a factor of the number in the square root.√12 = √(4 x 3) = √4 x √3 = 2√3√75 = √(25 x 3) = √25 x...

This is usually a good idea if you have an integral with two functions multiplied together when one of the functions differentiates to a constant (could take more than one differentiation).For example to ...