limit and continuous function

👨🏻‍🏫 學術台數學

chaotic_vampire_lord

2007-12-13 7:43 am

it is known that

lim(ln x) = ln(lim x)

since nature log function is continuous on (0,infinity)

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but why? are there any proof?

回答 (3)

魏王將張遼

2007-12-13 8:02 am

✔ 最佳答案

For generalization, we can state the theorem as follows on the basis of the definition of limit of a function:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec07/Crazylim2.jpg

And the proof is as follows:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec07/Crazylim3.jpg

參考: My Maths knowledge

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用戶219063

2007-12-19 5:09 am

For generalization, we can state the theorem as follows on the basis of the definition of limit of a function:

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用戶127502

2007-12-13 8:05 am

Definition of a continuous function :
lim(x->x*) f(x) = f(x*) and x* = lim(x->x*) x

參考: me

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