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1.Suppse f屬於C([a,b])∩C((a,b)) , f(a)=f(b)=0 and
lim f'(x) = lim f'(x) > 0 , show that f has at least one zero in (a,b).
x->a+ x->b-
2. Let D = {1/n : n in |N} and define the set in |R^2
E = ([0,1]X{0}) U ( DX[0,1] ) U {(0,1)}.
Explain whether E is connected or not.
3. Suppose a_k 屬於|R and |a_k|≦k for every positive integer k . Let
oo 1
f(x) = Σ (a_k)*x^k and f_n(x)= f(x + ---) .
k=1 n
Show that f_n converges uniformly to f on any [a,b]ㄈ(-1,1) .
麻煩請指教 謝謝
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