Find the following limit without using L'Hopital's Rule.
lim [x/(x - 1) - 1/(ln x)] when x tends to 1. (Note : This is a infinity - infinity form.)
Limit
2011-10-08 2:32 pm
回答 (2)
2011-10-08 4:55 pm
2011-10-08 2:58 pm
x/(x - 1) - 1/(ln x)
=x-(x-1)/(x-1)(ln x)
=1/(x-1)-(ln x)
So, when x tends to 1, both (x-1)&(ln x) tend to 0
The function tend to infinity
=x-(x-1)/(x-1)(ln x)
=1/(x-1)-(ln x)
So, when x tends to 1, both (x-1)&(ln x) tend to 0
The function tend to infinity
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