Search over 10,000 free study notes

Find two numbers that multiply together to equal the 3rd term and the product of the same two numbers also needs to equal the 2nd term. This is trial and error but in this case it will be,    (x - 4) (x -...

The first eigenvalue is 3, whose corresponding eigenvector is (1, 1), and the second eigenvalue is 2, whose corresponding eigenvector is (3, 4). In diagonal form, A = PDP^-1, where P = [[1, 3], [1, 4]] an...

In order to find the equation of the tangent to a curve at a point (x₁, y₁), we use the equation y - y₁ = m(x - x₁), where m is the gradient of the curve at (x<...

Unity just means 1, so we need to find all z such that z³=1. However, although we can immediately see that z=1 is a solution, when dealing with complex numbers some solution may not lie on the ...

Using the auxiliary equation t^2 - 2t - 3t = 0  t therefore is equal to 3 or -1. Using this value, a complementary function is derived.  Y= Ae^(3x) + Be^(-x). Finally, to fully solve, a particular integra...