1. Compare the graphics of the following functions, then prove the resulted inequality.
a) f (x) = ln (x + 1) and g (x) = x, ∀x∈(-1,∞)

b) f (x) = sin x, g (x) = x, ∀x∈[0,∞).

3. Having a rectangular box with dimensions of 10 cm and 20 cm, cut a square out of each corner, each the same size, so that by folding to obtain a rectangular box whose volume is the largest.

5. On the sides of the rectangle ABCD, with AB=a and BC=b, there are four points: M, N, P, Q such as AM = BN = CP = DQ = x. Which is the minimum area of the MNPQ parallelogram when x varies.