I'm trying to solve the limit limx→0+x−x−1x
I think we should use L'Hospital rule and the limit becomes
limx→0+−x−x(logx+1)=limx→0+logx+1−xx=+∞
Is it right?
I've tried to modify the form and not use L'Hospital's rule but without success.
Answer
Without the Hospital's rule: x−x−1x=−xx−1x⋅xx=−exlnx−1xlnx⋅lnx⋅1xx→+∞.
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