求lim(1/x+ln(1+e的x次方)/x其中x趋向于正无穷大

题目详情

求lim(1/x+ln(1+e的x次方)/x 其中x趋向于正无穷大

▼优质解答

答案和解析

lim[1/x+ln(1+e^x)]/x
=lim1/x^+limln(1+e^x)/x
=limln(1+e^x)/x
=limln(1+e^x)'
=lim(1+e^x)'/(1+e^x)
=lim(e^x)/(1+e^x)
=1

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