[單變] 幾題，出在"極限與連續"章節中

看板trans_math作者mercedesff (mercedesff)時間15年前 (2010/12/04 21:59)推噓0(0推 0噓 10→)

留言10則, 1人參與討論串1/1

以下想破頭，仍不得其解，請大大幫忙(跪)，謝謝! ╭ 1, if x=1; 1. Let f(x) = ┤ ╰ 2, if x=2. Is f a continuous function on its domain? Justify your answer. 2. Suppose that f:[a,b]→R is a continuous function. (a) Let a ≦ x_1 ＜ x_2 ≦ b . Prove that there is a point z 屬於 [a,b] such that f(x_1) + f(x_2) f(z) = 一一一一一一一一一一一 . 2 (b) Let a ≦ x_1 ＜ x_2 ＜ x_3 ≦ b . Prove that there is a point z 屬於 [a,b] such that f(x_1) + f(x_2) + f(x_3) f(z) = 一一一一一一一一一一一一一一一 . 3 3. Let f:(-∞,∞) → R be a continuous function such that there are two real numbers a and b, such that f(a) ≦ f(x) ≦f(b) for all -∞ ＜ x ＜ ∞ . Is the equation f(x) - x = 0 solvable ? ～～～～～ Justify your answer. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.113.90.123

→

kane950544

12/06 21:44, , 1^F

12/06 21:44, 1^F

→

kane950544

12/06 21:46, , 2^F

12/06 21:46, 2^F

→

kane950544

12/06 21:47, , 3^F

12/06 21:47, 3^F