Question: 1. Derive the chain rule using local linearization. [Hint: In other words, differentiate f(g(x)), using g(x + h) ≈ g(x) + g'(x)h and f(z + k) ≈ f(z) + f'(z)k.]
2. Use the Racetrack Principle and the fact that sin 0 = 0 to show that sin x ≤ x for all x ≥ 0.