sjlmsvv
幼苗
共回答了20个问题采纳率：90% 举报
解析,
lim(x→∞)(1+1/x)^x=e
lim(x→∞)[(2x+3)/(2x+1)]
=lim(x→∞)[1+1/(x+1/2)]^(x+1/2+1/2)
=lim(x→∞)[1+1/(x+1/2)]^(x+1/2)*lim(x→∞)[1+1/(x+1/2)]^(1/2)
=e*1
=e
1年前
追问
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ed9ka
举报
lim(x→∞)[1+1/(x+1/2)]^(1/2)这个为什么等于1
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举报
sjlmsvv
x→∞，1/(x+1/2)→0 故，[1+1/(x+1/2)]^(1/2)→1^(1/2)=1
