Question

吃小孩喇

微積分
求救

1. Complete the proof of the following question that we discussed in class:
Let f: (a, b) → R be a bounded function. Suppose that for all x₁, x2 = (a, b),
(f(x₁) + f(x2))
(x₁+x²) ≤
X2
2
Show that f is continuous on (a, b).
2. Let f [0, 1] → R be defined by
if x € Qºn [0, 1]
if x Qn [0, 1] and x =
E
f(x) =
0.
where p, q are relative prime positive integers
q'
Prove that f is continuous at each irrational number in [0, 1].