Find the limit of the following when x tends to infinity:
x ln(1 + 5/x + 6/x^2)
Limit
2011-01-20 3:04 am
回答 (2)
2011-01-20 4:15 am
✔ 最佳答案
As follows:圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/ScreenHunter_03Jan192014.gif
2011-01-25 4:45 am
x ln (1 + 5/x + 6/x^2)
=ln(1 + 3/x)^x (1 + 2/x)^x
as x-> infinity
this becomes ln (e^3 * e^2)
=ln (e^5)
=5
=ln(1 + 3/x)^x (1 + 2/x)^x
as x-> infinity
this becomes ln (e^3 * e^2)
=ln (e^5)
=5
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