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There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof.

The base case consists of proving that a statement is true for ...

tanh(x) = ((e^x-e^-x)/2)/((e^x+e^-x)/2) 1 - tanh²(x) = 1-((e^x-e^-x)/(e^x+e^-x))²  = ((e^2x+...

Answer : y = 3/x² + c/x⁴  Integrating factor is 4/x (1 mark) => I = e^{integral (4/x) dx} (1 mark) => I = x⁴ (1 mark). Using the f...

This took me some time to get my head around so I know what you mean. I always like to think of proof by induction like dominoes. Once you've pushed the first domino in line of dominos, you know it's goin...

The first step with this question is to expand all the brackets; this will produce the following equation:

2a + ai + 2b + bi = b + 1 + 10i + 2ai

The next step is to put all the terms which c...