(2) Let f(x) and g(x) be two continuous real-valued functions on [a,b]. Show that |(f(x)g(x))dx|2 ≤ ((|f(x)|2dx))((|g(x)|2dx). (15%)

(13) A logistic population model with relative growth rate 0.1 per year and carrying capacity 50 thousand can be expressed by the differential equation =0.1P(1 - ), with P in thousands and t in years. Given that the initial population is 9 thousand. Find the population size after 20 years. (If you memorized the formula, then you need to derive it for this problem.)