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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+...

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x³ + 2x² - 9x - 18. However it is very difficult to approach the problem like thi...

6x^2 + 7x + 2 can be written in the form ax^2 + bx + c. In order to factorise this I use the following method which can be used to factorise similar equations. Multiply 'a' and 'c' to get ac (here this is...

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...