lim(n趋向无穷){[(n^2+1)^(1/2)]/(n+1)}^n怎么解.

题目

lim(n趋向无穷){[(n^2+1)^(1/2)]/(n+1)}^n怎么解.

答案

lim e^{n[ln√(n²+1)-ln(n+1)]}
=lim e^{[ln√(n²+1)-ln(n+1)]/(1/n)} 应用洛必达法则
=lim e^[-(n-1)n²/(n+1)(n²+1)]
=1/e
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