... coefficient n! /( (n-r)! r! ). Define f(x) = (2 m)C0 + (2 m)C1 cos x + (2 m)C2 cos 2x + (2 m)C3 cos 3x + + (2 m)C(2m) cos 2mx. Let g(x) = (2 m)C0 + (2 m)C2 cos 2x + (2 m)C4 cos 4x + + (2 m)C(2m) cos 2mx. ... area PFCG = area PGDH. 5. Given that f(x) = (ax+b)/(cx+d), f(0) ≠ 0, f(f(0)) ≠ 0. Put F(x) = f( (f(x) ) (where there are n fs). If F(0) = 0, show that F(x) = x for all x where the expression ... 6. (1 ) Let I(x) = ∫cx f(x, u) du. Show that I'(x) = f(x, x) + ∫cx ∂f/∂x du. (2 ) Find limθ→0 cot θ sin(t sin θ). (3 ) Let G(t) = ∫0t cot θ sin(t sin θ) dθ. Prove that G&apos ;( /2)...