作者youyouyou (成大或台大噜~干)
看板trans_math
标题[考古] 成大考古( 不知年份 )
时间Thu Jun 16 21:56:25 2005
1 n 1
lim --- sigma --- = ?
n->oo n k=1 k
1 1
Is the integral S sin --- dx conergnet ? Justify your answer.
0+ x
Let f be differentiable for x>0. Prove or disprove
(i) If lim f(x) = 0 , then lim f'(x) = 0
x->oo x->oo
(ii) If lim f(x) = oo , then lim f'(x) = - oo
x->0+ x->0+
Find the Maclaurin series of f(x) =( 1+ x)^a,where a 属於 R.
Show that the function f(x) is analytic at x=0.
Find the 4-th order Taylor's expansion of sin(x+2y) at the point (0,0).
设函数 f:I -> R , 其中 I 为一非退化区间.
(a) 试证: 若 f 为连续, 则 f 必具反倒函数.
(b) 试问: 若 f 具反导函数, f 是否必为连续 ?
谢谢解答
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※ 编辑: youyouyou 来自: 140.115.213.118 (06/16 21:56)
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