P is the point representing the complex number
z = r( cos θ + i sin θ) in an argand diagram such
that ∣z−a∣∣z + a∣ = a^2 . Show that P moves on the curve
whose equation is r^2 =2a^2 cos2θ. sketch the curve
r^2 = 2a^2 cos 2θ , showing clearly the tangents at the pole.
Given the function f defined by f(x) = ((∣x−2∣)/(1−∣x∣))
(i) state the domain of f.
(ii) show that
f(x) = { ((((2−x)/(1+x)) , x < 0)),((((2−x)/(1−x)), 0 ≤ x < 2)),((((x−2)/(1−x)) , x ≥ 2)) :}
(iii) Investigate the continuity of f at x = 2.