Use Exercise 64 to prove that x tan x for 0 x < /2 and sin x x for x 0.

Use Exercise 64 to prove that x ≤ tan x for 0 ≤ x < π/2 and sin x ≤ x for x ≥ 0.

Data From Exercise 64

Prove that if ƒ(0) = g(0) and ƒ'(x) ≤ g'(x) for x ≥ 0, then ƒ(x) ≤ g(x) for all x ≥ 0. Show that the function given by y = ƒ(x) − g(x) is nonincreasing.