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下列命题中正确的是

A.

若

lim_{x \to x_{0}} f (x) ⩾ lim_{x \to x_{0}} g (x) \Rightarrow \exists δ > 0

, 当

0 < | x - x_{0} | < δ

时

f (x) ⩾ g (x)

.

B.

若

\exists δ > 0

使得当

0 < | x - x_{0} | < δ

时有

f (x) > g (x)

且

lim_{x \to x_{0}} f (x) = A_{0}, lim_{x \to x_{0}} g (x) = B_{0}

均

\exists

, 则

A_{0} > B_{0}

.

C.

若

\exists δ > 0

, 当

0 < | x - x_{0} | < δ

时

f (x) > g (x) \Rightarrow lim_{x \to x_{0}} f (x) ⩾ lim_{x \to x_{0}} g (x)

.

D.

若

lim_{x \to x_{0}} f (x) > lim_{x \to x_{0}} g (x) \Rightarrow \exists δ > 0

, 当

0 < | x - x_{0} | < δ

时有

f (x) > g (x)

.

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