a if is a continuous function that is positive on 0 0 and lim fx 0 the

Question

One of the following statements is true, and the other is false. Identify the false statement, and give a counter example (that is, an example demonstrating that the statement is false). (a) If ƒ is a continuous function that is positive on (0, ∞0) and lim f(x) = 0, then ƒ must eventually (1)be decreasing, (b) If ƒ is a continuous function that is positive on (0, ∞) and lim f(x) = 0, then f must eventually stay less than 10-100