求极限,答案到底是e^-1还是1 - 知识问答

求极限,答案到底是e^-1还是1

1个回答

lim【x→∞】[(2x-1)/(2x+1)]^x
=lim【x→∞】[(2x+1-2)/(2x+1)]^x
=lim【x→∞】[1-2/(2x+1)]^x
=lim【x→∞】[1-1/(x+1/2)]^x
=lim【x→∞】{[1-1/(x+1/2)]^(x+1/2)}/{[1-1/(x+1/2)]^(1/2)}
=1/e

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