Evaluate the limit.

👨🏻‍🏫 學術台數學

Ashie

2009-10-23 2:26 pm

Lim (ln x)/ sin (3πx)
x >1

Please evaluate the limit above. Use L/hospital Rule where appropriate.

I can't seem to get the right answer even thought I kept taking the derivative of the top and bottom.

Thanks in advance. =]

更新1:

For those of you that can't see, my question is: Lim (ln x)/ sin (3 pi x) x approaches 1

回答 (2)

cheungTim

2009-10-23 2:44 pm

✔ 最佳答案

Differentiate top and bottom.

Dx(ln x)=1/x
Dx(sin(3pi x))=3pi cos(3pi x)

Then, Sub 1 into x

Lim (1/1)/(3pi*cos(3pi*1))= -1/3pi

Answer is -1/3pi

參考: Myself

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Ashie

2009-10-23 2:56 pm

Thanks.

I got the same answer myself. =] I got realized cos 3 pi is 1. >

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