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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...

     (x+2) | (2x³+8x²+17x+18)         

=      2x²+4x+9

First, we factor out one (x+1). (1+x)^3 = (x+1)^2(x+1)= Then, we expand using the formula (a+b)^2 = a^2 + 2ab +b^2: =(x^2+2x+1)(x+1)= Then we multiply: = x^3 + 2x^2 + x + x^2 + 2x + 1 We sum the terms wit...