所屬科目：研究所、轉學考(插大)-高等微積分
(1.2) (2 points) If are bounded sequences in R, then
(1.4) (2 points) If A is connected inRn, thenA is also connected.
(1.6) (2 points) Let f be a continuous real function on R and let Z(f) be the set of all at which f(p) = 0. Then Z(f) is closed.
(1.7) (2 points) The function is uniformly continuous on (0, 1).
(1.8) (2 points) Let f be a real function on [0,2], then f is Riemann integrable on [0,2] if and only if|f| is Riemann integrable on [0, 2].
(1.10) (2 points) Let a uniformly convergent sequence of polynomials on [0,2] and . Then f is differentiable.
(2) (10 points) Let B = f{(x, y). Show that B is open set.
(3) (15 points) Let (M,d) be metric space and M. Show that the set {x1, x2, x3,...] is compact set.
(4) (20 points) Every rational t can be written in the form, where n> 0, and m and n are integers without any common divisors. When a = O, we take n = 1. Consider the function f defined on R by Prove that f is continuous at every irrational point, and that f has a discontinuity at every rational point.
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are bounded sequences in R, then
A is also connected.
at which f(p) = 0. Then Z(f) is closed.
is uniformly continuous on (0, 1).
a uniformly convergent sequence of polynomials on
[0,2] and 
. Then f is differentiable.
. Show that B is open set.
M.
Show that the set {x1, x2, x3,...] 
is compact set.
, where n> 0, and
m and n are integers without any common divisors. When a = O, we take n = 1.
Consider the function f defined on R by
