3) Prove ▽ × ( 0) = 0.
(2) Define the set A C 2 by s) n-0 (a) Prove that for any N 2 0 the set is compact. (b) Prove that for any є > 0 there exists some N > 0 so that for any x E A we have (c) Prove that A is totally bounded. (d) Prove that A is compact (2) Define the set A C 2 by s) n-0 (a) Prove that for any N 2 0 the set is compact....
11 > 0, then there exists a subset of A that is not Prove that if A CR and A Lebesgue measurable.
Prove that if ? is integrable on [?, ?] and ?(?) ≥ 0 for all ? in [?, ?], then [ f(x)dx > 0 7. Prove that if f is integrable on [a, b] and f(x) > 0 for all x in [a, b], then sof(x)dx > 0.
+o0 P(A,) 0(n N4 0, 2. Let A A = Q , prove i1 +o0 P(A,) 0(n N4 0, 2. Let A A = Q , prove i1
Prove that {19a +37b| : a,b E Z} = NU {0}. Prove that {19a +37b| : a,b E Z} = NU {0}.
Prove that: If「ム「OUT = 1 Then XouT+XL-0 and ROUT + RL=0 Prove that: If「ム「OUT = 1 Then XouT+XL-0 and ROUT + RL=0
Now assume that f(0) = 0 and f'(0) = 0. Prove that if f is twice differentiable and If"(x) < 1 for all x E R then 22 Vx > 0, f(x) < 2
3. Prove that (f = 0()] ^ [9 = 0(h)) = f =0(h).
Prove that (nC0)-(nC1)+(nC2)-....=0