X趋于无穷时,lim(2x+3/2x+1)^(x+1)等于多少,求详细过程
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X趋于无穷时,lim(2x+3/2x+1)^(x+1)等于多少,求详细过程
X趋于无穷时,lim(2x+3/2x+1)^(x+1)等于多少,求详细过程
X趋于无穷时,lim(2x+3/2x+1)^(x+1)等于多少,求详细过程
lim(x趋近于+∞)【[(2x+3)/(2x+1)]^(x+1)】
= lim(x趋近于+∞)【[(2x+1+2)/(2x+1)]^(x+1)】
= lim(x趋近于+∞)【[1+ 2/(2x+1)]^(x+1)】
= lim(x趋近于+∞)【[1+ 1/(x+1/2)]^(x+1/2) * [1+ 1/(x+1/2)]^(1/2) 】
= lim(x+1/2趋近于+∞)【[1+ 1/(x+1/2)]^(x+1/2) 】*lim(x+1/2趋近于+∞)【[ [1+ 1/(x+1/2)]^(1/2) 】
= e*1
= e
除以x
原式=(1+2/(2x+1))^(x+1)=(1+1/(x+1/2))^(x+1/2))(1+1/(x+1/2))^1/2=e
因:(1+1/(x+1/2))^(x+1/2))=e,且(1+1/(x+1/2))^1/2=1.
OK ==K O GG
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