微积分 黄丹 函数极限.pdf

GoBack §1 De?nition  f : Z+ → R    Note Example       one sided limit Left limit Heine De?nition  f : Z+ → R    Note Example       one sided limit Left limit Heine   f : D ?→ R, y = f (x) D  x0    1.1 (ε ? δ ) f (x) A   ?ε 0, ?δ 0, ?x ∈ N 0 (x , δ) | f (x) ? A | ε 0 De?nition  f : Z+ → R    Note Example       one sided limit Left limit Heine   f : D ?→ R, y = f (x) D  x0    1.1 (ε ? δ ) f (x) A   ?ε 0, ?δ 0, ?x ∈ N 0 (x , δ) | f (x) ? A | ε 0  f (x)  x → x0  A ??? ??? lim f (x) = A f (x) → A, x → x0 x→x0 1  1.1  f (x) = x sin , x = 0  lim f (x) = 0 x x→x0 1  1.1  f (x)