微積分[lim極限值]

👨🏻‍🏫 學術台數學

[匿名]

2011-05-19 4:54 pm

[ lim(x→∞) logx / √ x ] + 1 =?

更新1:

看到logx就卡住了請幫忙

回答 (4)

螞蟻雄兵

2011-05-19 5:11 pm

✔ 最佳答案

[ lim(x→∞)_logx /√ x ] + 1
Sol
logx=lnx/ln10
lim(x→∞)_logx /√ x
=(1/ln10)lim(x→∞)_lnx /x^(1/2) 0/0type
=(1/ln10)lim(x→∞)_(1/x)/[(1/2)x^(-1/2)]
=(2/ln10)lim(x→∞)_x^(1/2)/x
=(2/ln10)lim(x→∞)_(1/x^(1/2)
=0
So
[ lim(x→∞)_logx /√ x ] + 1
=1

but
lim(x→∞)_logx /(√ x + 1)=0

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[匿名]

2011-05-26 12:24 am

大部分的數學用書logx都是以e為底
以10為底的對數大多只用在估計上

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