limit

2012-04-13 11:28 pm
i want to ask

圖片參考:http://imgcld.yimg.com/8/n/HA04937267/o/701204130066413873393310.jpg
更新1:

and I want to ask 25X(infinity) > infinity?

更新2:

please give detailed explanation,thx

更新3:

do u mean 25(infinity) = infinity? thx

更新4:

thx for answering Q1 actually I don't understand why lim(n -> ∞) (1 + 1/25n)^(5n) will equal to lim(25n -> ∞) (1 + 1/25n)^(25n/5) please go to the following website: http://i615.photobucket.com/albums/tt234/chandaiman199111/question.jpg

更新5:

sorry.I have already understand.. Thx for answering my question.

回答 (3)

2012-04-14 5:07 am
✔ 最佳答案
1 lim(5x -> 5) (1 + 5x) = 1 + 5 = 6

2 lim(n -> ∞) (1 + 1/25n)^(5n)

= lim(25n -> ∞) (1 + 1/25n)^(25n/5)

= e^(1/5)
2012-04-18 12:26 am
1.
x-> 5, lim (1+5x) = 26

2.
5x->5 lim(1+5x) = lim (1+5) =6

3.
lim (1+1/25n)^5n = (lim (1+1/25n)^25n)^(1/5) = e^(1/5)

4.
25n -> infinity i.e. n -> infinity, 所以第四條都係 e^(1/5)
2012-04-14 1:39 am
25X(infinity) ---> infinity


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