The curve C has equation y = (2x² + kx)/(x+1), where k is a constant. Find the set of values of k for which C has no stationary points. For the case k = 4, find the equations of the asymptotes of C and sketch C, indicating the coordinates of the points where C intersects the coordinate axes.

The curve C has equation `y = (x² + px + 1)/(x - 2)`, where p is a constant. Given that C has two asymptotes, find th...

The curve C has equation y = λx + x/(x – 2), where λ is a non-zero constant.

The curve C has equation y = (3x - 9) / ((x - 2)(x + 1)).

The cubic equation x³ +bx² +cx+d = 0, where b, c and d are constants, has roots α, β and γ. It is given that α+β + γ ...

The sequence of positive numbers u₁, u₂, u₃, ... is such that u₁ < 5 and, for n ≥ 1, u(n+1) = (6u(n) + 5) / (u(n) + 2)

Let k and m be non-zero constants. The matrices A, B and C are given by A = [[0,1],[-1,1],[1,1]], B = [[k,0],[0,m]], ...